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Basic representations of some affine Lie algebras and generalized Euler identities

Part of: Lie algebras and Lie superalgebras Combinatorics

Published online by Cambridge University Press:  09 April 2009

Kailash C. Misra
Kailash C. Misra
Affiliation:
Department of MathematicsNorth Carolina State UniversityRaleigh, North Carolina 27695-8205, U. S. A.
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Abstract

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We consider certain affine Kac-Moody Lie algebras. We give a Lie theoretic interpretation of the generalized Euler identities by showing that they are associated with certain filtrations of the basic representations of these algebras. In the case when the algebras have prime rank, we also give algebraic proofs of the corresponding identities.

MSC classification

Secondary: 17B65: Infinite-dimensional Lie (super)algebras 05A19: Combinatorial identities, bijective combinatorics
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 42 , Issue 3 , June 1987 , pp. 296 - 311
Copyright
Copyright © Australian Mathematical Society 1987

References

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