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Multipartitions, generalized Durfee squares and affine Lie algebra characters

Part of: Combinatorics Quantum field theory; related classical field theories Lie algebras and Lie superalgebras

Published online by Cambridge University Press:  01 August 2017

Peter Bouwknegt
Peter Bouwknegt*
Affiliation:
Department of Physics and Mathematical Physics, University of Adelaide, Adelaide SA 5005, Australia e-mail: [email protected]
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Abstract

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We give some higher dimensional analogues of the Durfee square formula and point out their relation to dissections of multipartitions. We apply the results to write certain affine Lie algebra characters in terms of Universal Chiral Partition Functions.

MSC classification

Secondary: 05A17: Partitions of integers 05A19: Combinatorial identities, bijective combinatorics 17B67: Kac-Moody (super)algebras; extended affine Lie algebras; toroidal Lie algebras 81T40: Two-dimensional field theories, conformal field theories, etc.
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 72 , Issue 3 , June 2002 , pp. 395 - 408
Copyright
Copyright © Australian Mathematical Society 2002

References

[1] Andrews, G. E., ‘Generalizations of the Durfee square’, J. London Math. Soc. 3 (1971), 563–570.Google Scholar
[2] Andrews, G. E., The theory of partitions. Encyclopedia Math. Appl. 2 (Addison-Wesley, Reading, 1976).Google Scholar
[3] Andrews, G. E., Partitions: Yesterday and today (New Zealand Mathematical Society, Wellington, 1979).Google Scholar
[4] Ardonne, E., Bouwknegt, P., Guruswamy, S. and Schoutens, K., ‘ K-matrices for non-Abelian quantum Hall states’, Phys. Rev. B61 (2000), 10298-10302 [cond-mat/9908285].Google Scholar
[5] Ardonne, E., Bouwknegt, P. and Schoutens, K., ‘Non-Abelian quantum Hall states—exclusion statistics, K-matrices and duality - ‘ , J. Stat. Phys. 102 (2001), 421–469.CrossRefGoogle Scholar
[6] Berkovich, A. and McCoy, B., ‘The universal chiral partition function for exclusion statistics’, in: Statistical Physics on the Eve of the 21st Century (eds. Batchelor, M. T. and Wille, L. T.) Series on Adv. in Stat. Mech. 14 (World Scientific, Singapore, 1999) pp. 240–256. [hep-th/9808013].Google Scholar
[7] van Elburg, R. and Schoutens, K., ‘Quasi-particles in fractional quantum Hall effect edge theories’, Phys. Rev. B58 (1998), 15704 [cond-mat/9801272].Google Scholar
[8] Hardy, G. H. and Wright, E. M., An introduction to the theory of numbers (Oxford University Press, Oxford, 1960).Google Scholar
[9] Kac, V. G., Infinite dimensional Lie algebras (Cambridge University Press, Cambridge, 1985).Google Scholar
[10] Sylvester, J. J., A constructive theory of partitions, arranged in three acts, an interact and an exodion. Collected works. Vol. 4 (Cambridge University Press, Cambridge, 1912).Google Scholar