1

Publications

 

Edited Books

 

B1. R.C. King, M. Bylicki and J. Karwowski, Symmetry, Spectroscopy and SCHUR, Proceedings of Prof B.G, Wybourne Commemorative Meeting, Torun.  Nicolaus Copernicus University Press, Torun, (2006), i-iv, 1-382

 

Please refer to the Notes of Guidance for the format of publications listings. 

Conference Papers

 

C1. King R.C. Branching rules using tensor methods, Proceedings of 4th ICGTMP  Nijmegen: University of Nijmegen, 1975, 400‑408.

 

C2. King R.C. Kronecker products and modification rules for spin representations  Proceedings of 4th ICGTMP 2 Nijmegen: University of Nijmegen, 1975, 572‑574.

 

C3. King R.C.  Spinor representations, Lecture Notes in Physics 50, Berlin: Springer, 1976, 481‑489.

 

C4. King R.C.  Weight multiplicities for the classical groups, Lecture Notes in Physics 50, Berlin: Springer, 1976, 490‑499.

 

C5. King R.C. and Qubanchi A.H.A.  Branching rule  SO(7) G2, Lecture Notes in Physics 79, Berlin: Springer, 1978, 497‑499.

 

C6. King R.C. and Qubanchi A.H.A.  Weight multiplicities of the exceptional Lie groups, Lecture Notes in Physics 94 Berlin: Springer, 1979, 530‑531.

 

C7. King R.C.  U(1) factors in branching rules, Physica 114A, 1982, 345‑349.

 

C8. King R.C.  Group theory of unified gauge models and tumbling, Physica 114A, 1982 393‑397.

 

C9. King R.C.  Generalised Young tableaux for Lie algebras and superalgebras

     Lecture Notes in Physics 180 Berlin: Springer, 1983, 41‑47.

 

C10. King R.C.  Supersymmetric functions and the Lie supergroup U(m/n), Ars Comb 16A, 1983, 269‑287.

 

C11. King R.C.  Young diagram techniques and representations of classical Lie groups and supergroups, Proceedings of 14th ICGTMP, Ed Y M Cho, Singapore: World Scientific Pub, 1986, 199‑204.

    

C12. King, R.C. String and superstring spectra.  In Symmetries in Science III, Ed. B. Gruber. Plenum Press, New York, 1989, 545-558.


C13. King, R.C. S‑functions and characters of Lie algebras and superalgebras. In Invariant theory and tableaux, Ed. D. Stanton, Vol. 19 of IMA Volumes in Mathematics and its Applications, Springer‑Verlag, New York, 1989, 226-261.

 

C14. Van der Jeugt J., Hughes J.W.B., King R.C. and Thierry-Meig J. Representations of sl(m/n) and their characters.  In Proceedings of the CMS Seminar on Lie theory, differential equations and representation theory, Ed. V. Hussin, CRM, Montreal, 1990, 233-252.

 

C15. King R.C. S-functions and characters of Lie algebras and Lie groups.  In Topics in Algebra: Part 2 Commutative Rings and Algebraic Groups, Eds. S. Balcerzyk, T. Josefiak, J. Kerempa, D. Simson and W. Vogel, Banach Center Publications, Vol. 26, PWN-Polish Scientific Publishers, Warsaw, 1990, 327-344.

 

C16. King R.C., Van der Jeugt J., Hughes J.W.B. and Thierry-Mieg J. Atypical modules of the Lie superalgebra gl(m/n).  In Group Theoretical Methods in Physics, Proceedings, Moscow, 1990, Ed. V.V. Dodonov and V.I. Man'ko, Lecture Notes in Physics Vol 382, Springer-Verlag, 1991, 512-515.

 

C17. King R.C., Hughes J.W.B. and Van der Jeugt J. The composition factors of Kac modules of sl(M/N).  In Group Theoretical Methods in Physics, Proceedings, Moscow, 1990, Ed. V.V. Dodonov and V.I. Man'ko, Lecture Notes in Physics Vol. 382, Springer-Verlag, Berlin, 1991, 522-526.

 

C18. King R.C. and Welsh T.A. Tensor products for affine Kac Moody algebras.  In Group Theoretical Methods in Physics, Proceedings, Moscow, 1990, Ed. V.V. Dodonov and V.I. Man'ko, Lecture Notes in Physics vol 382, Springer-Verlag, Berlin, 1991, 508-511.

 

C19. Fulling S.A., Cummins C.J., King, R.C. and Wybourne B.G. Group-theoretical classification of polynomial functions.  In Classical and Quantum Systems - Foundations and Symmetries, Ed. H-D. Doebner, W. Scherer and F. Schroeck, World Scientific Publishing, Singapore, 1993, 362-365

 

C20. Cummins C.J. and King R.C. Characters of Hecke algebras of type An-1: I. The generic case.  In Group Theoretical Methods in Physics, Proceedings, Salamanca, 1992, Vol I, Eds. M.A. del Olmo, M. Santander and J. Mateos Guilarte, CIEMA/RSEF, Madrid, 1993, 363-366.

 

C21. Cummins C.J. and King R.C. Characters of Hecke algebras of type An-1: II. The non-generic case.  In Group Theoretical Methods in Physics, Proceedings, Salamanca, 1992, Vol I, Eds. M.A. del Olmo, M. Santander and J. Mateos Guilarte, CIEMA/RSEF, Madrid, 1993, 367-370.

 

C22. King R.C. Lie superalgebras: their representations and an application to a supersymmetric quantum spin chain model.  In Symmetries and Structural Properties of Condensed Matter, Eds. W. Florek, D. Lipinski and T. Lulek, World Scientific Press, Singapore, 1993, 55-66.


C23. King R.C. Hecke algebras: their representations and an application to a supersymmetric quantum spin chain model.  In Symmetries and Structural Properties of Condensed Matter, Eds. W. Florek, D. Lipinski and T. Lulek, World Scientific Press, Singapore, 1993, 57-78.

 

C24. King R.C. and Welsh T.A.  Representations of quantum algebras.  In Symmetries and Structural Properties of Condensed Matter, Eds. W. Florek, D. Lipinski and T. Lulek, World Scientific Press, Singapore, 1995, 183-196.

 

C25. Hussin A. and King R.C. Characters of affine Kac-Moody algebras.  In Group 21, Eds. H.-D.Doebner, P. Nattermann and W. Scherer, World Scientific , Singapore, 1997, 157-166.

 

C26. Hussin A. and King R.C. Affine Kac-Moody algebras and their representations.  In Symmetries and Structural Properties of Condensed Matter, Eds. T. Lulek, W. Florek and B. Lulek, World Scientific Publishing, Singapore, 1997, 296-309.

 

C27.  King R.C. Some analogies between the representation theory of SO(2n) and Sp(2n). In Symmetries and Structural Properties of Condensed Matter V, Eds. T. Lulek, W. Florek and B. Lulek, World Scientific Publishing, Singapore, 1999, 138-151.

 

C28. King R.C. Weight multiplicities and branching rules for simple and affine Lie algebras. In Algebraic Methods in Physics: A Symposium for the 60th Birthdays of  Jiri Patera and Pavel Winternitz, Eds. Y Saint-Aubin and L. Vinet, CRM Series in Mathematical Physics, New York, USA, Springer-Verlag, 2001, pp 121-133.

 

C29.  King R.C. Weyl's denominator identity and its deformations. In Symmetries and Structural Properties of Condensed Matter VI, Eds. T. Lulek, B. Lulek and A. Wal, World Scientific Publishing, Singapore, 2001, 138-151.  

 

C30. King R.C. Progress on numerator formulae expansions for Kac-Moody algebras. Annals of Combinatorics, 5, 2001, 381-395.

 

C31. Burdik C., King R.C. and Welsh T.A. The explicit construction of irreducible representations of the quantum algegra U_q(sl(n)). In New Developments in Fundamental Interaction Theories, 37th Karpacz Winter School in Theoretical Phyics, Karpacz, Poland. AIP Conference Proceedings 589, 158-169, New York, USA, American Institute of Physics, 2001

 

C32.  King R.C., Tollu C. and Toumazet F., Stretched Littlewood-Richardson coefficients and Kostka coefficients. In Symmetry in Physics. In Memory of Robert T Sharp. Eds. P Winternitz, J Harnad, C S Lam and J Patera, CRM Proceedings and Lecture Notes, 34, 99-112, 2004.

 

C33.   King R.C., Palev T.D., Stoilova N.I. and Van der Jeugt J.,  On the n-particle Wigner quantum oscillator: non-commutative coordinates and particle localisation. In  Lie Theory and its Applications in Physics V,  Proceedings of the Fifth International Workshop, Varna, Bulgaria 16-22 June 3003. Eds: H-D Doebner and V Dobrev, Singapore, World Scientific Publishing 2004, 327-341.

C34.   King R.C., Palev T.D., Stoilova N.I. and Van der Jeugt J., The n-particle Wigner quantum oscillator: non-commutative coordinates and physical properties,
In Proceedings of the 25th ICGTMP, Cocoyoc, Mexico, 2005. Eds. G.S. Pogosyan, L.G. Vincent and K.B. Wolf. Institute of Physics Conference Series 185, Bristol, IoP Publishing, 2005, 545-550

C35.  Fauser B., Jarvis P.D. and King R.C., A Hopf algebraic approach to the theory of group branchings, In Symmetry, Spectroscopy and SCHUR, Proceedings of Prof B.G, Wybourne Commemorative Meeting, Torun. Eds: R.C. King, M. Bylicki and J. Karwowski, Nicolaus Copernicus Univ Press, Torun, (2006), 75-86

C36.   King R.C., Brian Wybourne and Schur functions, In Symmetry, Spectroscopy and SCHUR, Proceedings of Prof B.G, Wybourne Commemorative Meeting, Torun. Eds: R.C. King, M. Bylicki and J. Karwowski, Nicolaus Copernicus Univ Press, Torun (2006), 163-171

C37.  Welsh T.A., Jarvis P.D. and King R.C., Invariants of mixed qubit systems, In Symmetry, Spectroscopy and SCHUR, Proceedings of Prof B.G, Wybourne Commemorative Meeting, Torun. Eds: R.C. King, M. Bylicki and J. Karwowski, Nicolaus Copernicus Univ Press, Torun, (2006), 315-323.

C38.  King R.C. and Welsh T.A., Qubits and invariant theory, J Physics: Conference Series, “Symmetry and Structural Properties of Condensed Matter (SSPCM 2005)”, 30 (2006), 1-8.

C39.  King R.C. and Welsh T.A., Mixed two-qubit system and invariant theory, In Quantum Theory and Symmetries IV, Vol 2. Ed. V.K. Dobrev, Heron Press, Sofia, 2006, pp671-682.

C40. King R.C., Tollu C. and Toumazet F., The hive model and the factorisation of Kostka coefficients, Seminaire Lotharingien Comb.  54A (2006) B54Ah.

C41. King R.C., Tollu C. and Toumazet F., The hive model and the polynomial nature of stretched Littlewood-Richardson coefficients,  Seminaire Lotharingien Comb. 54A (2006) B54Ad.

C42. King R.C., Fauser, B. and Jarvis, P.D., Hopf algebras and characters of classical groups, in “Symmetry and Structural Properties of Condensed Matter, 5–12 September 2007, Myczkowce, Poland”, Eds: T Lulek, A Wal and B Lulek, J Phys: Conf Ser. 104 (2008) 012030

 

 

 

 

 

 

 

 


 

 

5    Conference Contributions - Other

 

O1.  King R.C.  Departmental review: coping with assessment fatigue.  In Proceedings of Departmental Review in Higher Education, Eds: Aylett, R.P.T. and Gregory, K.J. Goldsmiths College, London, 1996, 75-82.

 

 

6    Departmental Working Papers

 

U1. King R.C., Lanou R.E. and Tuan S.F. Low energy K-nucleon interactions II, Internal Report 101, Physics Dept, Brown University, USA, 1961.

 

U2. King R.C. Eigenvalues of generalised Casimir operators of semisimple Lie groups, Preprint 18, Maths Dept, University of Southampton, England, 1978.

 

U3. Cummins C.J. and King R.C. The Higgs potential of the 75 of SU(5) revisited: non‑maximal and disconnected symmetry breaking, Preprint, Maths Dept, University of Southampton, England, 1982.

 

U4. Cummins C.J. and King R.C. Some noteworthy S‑function identities, Preprint Centre des Recherche Mathematiques, Universite de Montreal, Canada, 1987.

 


11  Journal Papers - Academic Journals

1.   King R.C., Lanou R.E. and Tuan S.F. Low energy   interactions, Phys Rev Lett, 6, 1961, 500‑504.

 

2.   Franklin J., King R.C. and Tuan S.F. Possible theoretical interpretations of the excited hyperons, Phys Rev, 124, 1961, 1995‑1999.

 

3.   King R.C. Production of cascade particles, Nuovo Cimento, 30, 1963, 1220‑1244.

 

4.   King R.C. Production and decay of decuplet baryon resonances and broken U(6,6) symmetry, Nuovo Cimento, 50, 1967, 719‑740.

 

5.   Caudrey P.J., Ketley I.J. and King R.C. Covariant arbitrary‑spin wave functions and helicity couplings, Nucl Phys, B6, 1968, 671‑686.

 

6.   Abramsky Y.J. and King R.C.  Missing SU(3) multiplets and SU(6,6) selection rules, Phys Rev Lett 20; 21, 1968, 506E, 1408‑1410.

 

7.   Abramsky Y.J. and King R.C.  Formation and decay of negative parity baryon resonances in a broken U(6,6) model, Nuovo Cimento A67, 1970, 153‑216.

 

8.   King R.C.  Generalised Young tableaux and the general linear group, J Math Phys 11, 1970, 280‑294.

 

9.   King R.C.  The dimensions of irreducible representations of linear groups, Can J Math 22. 1970, 436‑448.

 

10. King R.C.  The dimensions of irreducible tensor representations of the orthogonal and symplectic groups, Can J Math 23, 1971, 176‑188.

 

11. King R.C.  Modification rules and the products of irreducible representations of the unitary, orthogonal and symplectic groups, J Math Phys 12, 1971, 1588‑1598.

 

12. King R.C. and Plunkett S.P.O.  The evaluation of branching rules for linear groups using mappings between weight spaces, J de Physique 33, 1972, 145‑153.

 

13. Abramsky Y.J., Jahn H.A. and King R.C.  Frobenius symbols and the groups Ss GL(n), O(n) and Sp(n), Can J Math 25, 1973, 941‑959.

 

14. Butler P.H. and King R.C.  Branching rules for U(N)U(M) and the evaluation of outer plethysms, J Math Phys 14, 1973, 741‑745.

 

15. Butler P.H. and King R.C.  The symmetric group: characters, products and plethysms, J Math Phys 14, 1973, 1176‑1183.

 

16. King R.C.  Branching rules for GL(N) 1 and the evaluation of inner plethysms, J Math Phys 15, 1974, 258‑267.

 

 

17. Butler P.H. and King R.C.  Symmetrised Kronecker products and group representations, Can J Math 6, 1974, 328‑339.

 

18. King R.C.  Generalised Vandermonde determinants and Schur functions, Proc Amer Math Soc 48, 1975, 53‑56.

 

19. King R.C.  Branching rules for classical Lie groups using tensor and spinor methods, J Phys A8, 1975, 429‑449.

 

20. King R.C. and Plunkett S.P.O.  The evaluation of weight multiplicities using characters and S‑functions, J Phys A8, 1976, 863-887.

 

21. King R.C. and Al-Qubanchi A.H.A.  The branching rule for the restriction from SO(7) to G2, J Phys A11, 1978, 1-7.

 

22. King R.C. and Al‑Qubanchi A.H.A.  The evaluation of weight multiplicities of G2,  J Phys A11, 1978, 1491‑1499.

 

23. El‑Samra N. and King R.C.  Reduced determinantal forms for characters of the classical Lie groups, J Phys A12, 1979, 2305‑2315.

 

24. El‑Samra N. and King R.C.  Dimensions of irreducible representations of the classical Lie groups, J Phys A12, 1979, 2317‑2328.

 

25. Englefield M.J. and King R.C.  Symmetric power sum expansion of the eigenvalues of generalised Casimir operators of semi‑simple Lie groups, J Phys A13, 1980, 2297‑2317.

 

26. King R.C.  Unitary group subjoinings, J Phys A13, 1980, 3563‑3583.

 

27. El‑Sharkaway N.G., Jahn H.A. and King R.C.  New integral bases for symmetric functions, C R Math Rep Acad Sci Canada 2, 1980,  243‑246.

 

28. King R.C. and Al‑Qubanchi A.H.A.  Natural labelling schemes for simple roots and irreducible representations of exceptional Lie algebras, J Phys A14, 1981, 15‑49.

 

29. King R.C. and Al‑Qubanchi A.H.A.  The Weyl groups and weight multiplicities of the exceptional Lie groups, J Phys A14, 1981, 51‑75.

 

30. King R.C.  Kronecker products of representations of exceptional Lie groups,  J Phys A14, 1981, 77-83.

 

31. El‑Sharkaway N.G., Jahn H.A. and King R.C.  Regular products of the single‑hook characters of the unitary group, J Phys A14, 1981, 1557‑1566.

 

32. Bowler K.C., Corvi P.J., Hey A.J.G., Jarvis P.D. and King R.C.  The role of Sp(12,R) in the harmonic oscillator quark model, Phys Rev D24, 1981, 197‑215.

 

33. King R.C.  Fundamental fermion representations in generalisations of the SU(5) grand unified gauge theory, Nucl Phys B185, 1981, 133‑156.

 

 

34. King R.C., Luan Dehuai and Wybourne B.G.  Symmetrised powers of rotation group representations, J Phys A14, 1981, 2509‑2538.

 

35. King R.C.  The character generator of Sp(2k), C R Math Rep Acad Sci Canada 3, 1981, 149‑153.

 

36. King R.C. and Wybourne B.G.  Some noteworthy spin plethysms, J Phys A15, 1982, 1137‑1142.

 

37. King R.C., Patera J. and Sharp R.T.  On finite and continuous little groups of representations of semisimple Lie groups, J Phys A15, 1982, 1143‑1158.

 

38. King R.C. and El‑Sharkaway N.G.I.  The character generators of SO(2k) and SO(2k+1), C R Math Rep Acad Sci Canada 4, 1982, 299‑304.

 

39. Black G.R.E., King R.C. and Wybourne B.G.  Kronecker products for compact semisimple Lie groups, J Phys A16, 1983, 1555‑1589.

 

40. King R.C. and El‑Sharkaway N.G.I.  Standard Young tableaux and weight multiplicities of the classical Lie groups, J Phys A16, 1983, 3153‑3178.

 

41. King R.C. and El‑Sharkaway N.G.I.  Standard Young tableaux and character generators of the classical Lie groups, J Phys A17, 1984, 19‑45.

 

42. Cummins C.J. and King R.C.  Symmetry breaking patterns for third‑rank totally antisymmetric tensor representations of unitary groups, J Phys A17, 1984, L627‑633

 

43. King R.C.  Young tableaux, Schur functions and SU(2) plethysms, J Phys A18, 1985, 2429‑2440.

 

44. King R.C. and Wybourne B.G.  Holomorphic discrete series and harmonic unitary irreducible  representations of non‑compact Lie groups: Sp(2n,R), U(p,q) and SO(2n), J Phys A18, 1985, 3113‑3139.

 

45. Cummins C.J. and King R.C.  Absolute minima of the Higgs potential for the 75 of SU(5), J Phys A19, 1986, 161‑181.

 

46. Barnes K.J., King R.C.and Surridge M.  Dimensional reduction, spontaneous symmetry breaking and the absence of chiral fermions, Nucl Phys B281, 1987, 253‑268.

 

47. Cummins C.J. and King R.C.  Young diagrams, supercharacters of OSp(M/N) and modification rules, J Phys A20, 1987, 3103‑3120.

 

48. Cummins C.J. and King R.C.  Composite Young diagrams, supercharacters of U(M/N) and modification rules, J Phys A20, 1987, 3121‑3133.

 

49. Hughes J.W.B. and King R.C. A conjectured character formula for atypical irreducible modules of the Lie superalgebra sl(m/n), J. Phys., A20, 1987, L1047‑L1052.

 

 

50  Rao K.S., Rajeswari V. and King R.C. Solutions of Diophantine equations and degree-one polynomial zeros of Racah coefficients, J. Phys., A21, 1988, 1959‑1970.

 

51  Farmer R.J., King R.C. and Wybourne B.G. Spectrum-generating functions for strings and superstrings, J. Phys., A21, 1988, 3979‑4007.

 

52  King R.C., Wybourne B.G. and Yang M. Slinkies and the S-function content of certain generating functions, J. Phys., A22, 1989, 4519‑4535.

 

53  Van der Jeugt J., Hughes J.W.B., King R.C. and Thierry-Mieg J. A character formula for singly atypical modules of the Lie superalgebra sl(m/n),  Communications in Algebra, 18, 1990, 3453-3480.

 

54  Van der Jeugt J., Hughes J.W.B., King R.C. and Thierry-Mieg J. Character formulas for irreducible modules of the Lie superalgebras sl(m/n), J. Math. Phys., 31, 1990, 2278-2304.

 

55  King R.C. and Wybourne B.G. Characters of Hecke Algebras  Hn(q) of type  An-1, J. Phys., A23, 1990, L1193-L1197.

 

56  King R.C. and Wybourne B.G. Representations and traces of the Hecke algebras Hn(q) of type An-1, J. Math. Phys., 33, 1992, 4-14.

 

57  Hughes J.W.B., King R.C. and Van der Jeugt J. On the composition factors of Kac-modules for the Lie superalgebras sl(m/n), J. Math. Phys. 33, 1992, 470-491.

 

58  King R.C., Fulling S.A., Wybourne B.G. and Cummins C.J. Normal forms for tensor polynomials: I. The Riemann tensor, Classical and Quantum Gravity 9, 1992, 1151-1197.

 

59  Cummins C.J. and King R.C. Characters of An-1 Hecke algebras at roots of unity, J.Phys., A25, 1992, L789-L797.

 

60  King R.C. and Welsh T.A. Construction of graded covariant GL(m/n)-modules using tableux, Journal of Algebraic Combinatorics, 1, 1992, 151-170.

 

61  King R.C. and Welsh T.A. Construction of orthogonal group modules using tableaux, Linear and Multilinear Algebra, 33, 1993, 251-283.

 

62  King R.C. and Welsh T.A. Construction of GL(n)-modules using composite tableaux, Linear and Multilinear Algebra, 34, 1993, 99-122.

 

63  Cummins C.J. and King R.C. Frobenius formula for the characters of Hecke algebras Hn(q) at roots of unity, Communications in Algebra, 21, 1993, 4397-4423.

 

64  Cummins C.J. and King R.C. An algorithm for calculating characters of Hecke algebras Hn(q) of type An-1 when q is a root of unity, Communications in Algebra, 21, 1993, 4425-4437.

 

65  Hussin A., King R.C., Leng X. and Patera J. Graded contractions of the affine Lie algebra A1(1), its representations and tensor products, and an application to the branching rule A1(1)  A1(1), J Phys, A27, 1994, 4125-4152.

 

 

66  Cummins C.J. and King R.C. WZW fusion rules for the classical Lie algebras, Canadian Journal of Physics, 72, 1994, 342-344.

 

67  King R.C. and Wybourne B.G. The place of the adjoint representation in the Kronecker square of irreducible representations of simple Lie groups, J Phys A, 29, 1996, 5059-5077.

 

68  King R.C. and Wybourne B.G. Products and symmetrized powers of irrrreducible representations of Sp(2n,R) and their associates,  J Phys A, 31, 1998, 6669-6689.

 

69  King R.C., Toumazet F. and Wybourne B.G. Products and symmetrized powers of irreducible representations of SO*(2n), J Phys A, 31, 1998, 6691-6705.

 

70  King R.C., Toumazet F. and Wybourne B.G. A finite subgroup of the exceptional Lie group G2,  J Phys A, 32, 1999, 8527-8537

 

71  King R.C. and Wybourne B.G. Analogies between finite-dimensional irreducible representations of SO(2n) and infinite-dimensional irreducible representations of Sp(2n,R) Part I: Characters and products, J Math Phys, 41, 2000, 5002-5019.

 

72  Yucai Su, Hughes J.W.B. and King R.C. Primitive vectors of Kac-modules of the Lie superalgebras sl(m/n),  J Math Phys, 41, 2000, 5064-5087. 

 

73  King R.C. and Wybourne B.G. Analogies between finite-dimensional irreducible representations of SO(2n) and infinite-dimensional irreducible representations of Sp(2n,R) Part II: Plethysms, J Math Phys, 41, 2000, 5656-5690

 

74  King R.C. and Wybourne B.G.  Multiplicity free tensor products of irreducible representations of the exceptional Lie groups, J Phys A, 35, 2002, 3489-3513.

 

75  Hamel A.M. and King R.C.  Symplectic shifted tableaux and deformations of Weyl's denominator formula for sp(2n). J Algebraic Combinatorics, 16, 2002, 269-300.

 

76  King R.C., Palev T.D., Stoilova N.I. and Van der Jeugt J.  The non-commutative and discrete spatial structure of a 3D Wigner quantum oscillator, J Phys A, 36, 2003, 4334-4362

 

77  King R.C., Palev T.D., Stoilova N.I. and Van der Jeugt J. A non-commutative n-particle 3D Wigner quantum oscillator, J Phys A, 36, 2003, 11999-12019

 

78    King R.C., Toumazet F. and Wybourne B.G. The square of the Vandermonde determinant and its q-generalisation,  J Phys A, 37, 2004, 735-767

 

79    Hamel A.M. and King R.C. U-turn alternating sign matrices, symplectic shifted tableaux and their weighted enumeration. J Algebraic Combinatorics, 21 (2005), 395-421

 

80    Fauser B., Jarvis P.D., King R.C. and Wybourne B.G., New branching rules induced by plethysm, J. Phys. A: Math. Gen. , 39 (2006), 2611-2655

81    King R.C.,  Stoilova N.I. and Van der Jeugt,  Representations of the Lie superalgebra gl(1|n) in a Gel'fand-Zetlin Basis and Wigner Quantum Oscillators. J Phys A: Math Gen, 39 (2006), 5763-5785

 

82    Frey J.G., King R.C and Moss R.E., Multiphoton transitions for the harmonic oscillator, Molecular Physics, 104 (2006), 2523-2525.

 

83    King R.C.and Welsh T.A., Coloured generalised Young diagrams for affine Weyl-Coxeter groups, Electronic J. Combinatorics, 14 (2007), R13 1-64.

84    Hamel A.M. and King R.C. Bijective proofs of shifted tableau and alternating sign matrix identities. J. Algebraic Combinatorics, 25 (2007) 417-458.

 

85    King R.C., Welsh T.A. and Jarvis P.D., The mixed two-qubit system and the structure of its ring of local invariants, J Phys A. 40 (2007) 10083-10108.

 

 

86    King R.C., Welsh T.A. and Van Willigenburg S.J., Schur positivity of skew Schur function differences and applications to ribbons and Schubert classes,  J. Algebraic Combinatorics, 28 (2008) 139-167.

 

Accepted for publication:

 

87    King, R.C., Tollu, C. and Toumazet F., Factorisation of Littlewood-Richardson coefficients, J Combinatorial Theory A (2008) http://dx.doi.org/10.1016/j.jcta.2008.06.005

 

            Submitted papers:

 

88    Fauser B., Jarvis P.D. and King R.C., Hopf algebra structure of the character rings of orthogonal and symplectic groups, submitted to J Algebra.

 

            Unpublishd:

 

89    Dou, D.Q.J., Tang, R.L. and King, R.C., A hive model determination of multiplicity-free Schur function products and skew Schur functions