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Proceedings of the National Academy of Sciences of the United States of America logoLink to Proceedings of the National Academy of Sciences of the United States of America
. 1978 Feb;75(2):578–579. doi: 10.1073/pnas.75.2.578

Lie algebras and classical partition identities

J Lepowsky 1,*, S Milne 1
PMCID: PMC411298  PMID: 16592491

Abstract

In this paper we interpret Macdonald's unspecialized identities as multivariable vector partition theorems and we relate the well-known Rogers—Ramanujan partition identities to the Weyl—Kac character formula for an infinite-dimensional Euclidean generalized Cartan matrix Lie algebra.

Keywords: Macdonald identities, Rogers—Ramanujan identities, Weyl—Kac character formula, generalized Cartan matrix Lie algebras

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