Lie algebras and classical partition identities

1 February 1978

journal article
research article
Published by Proceedings of the National Academy of Sciences in Proceedings of the National Academy of Sciences of the United States of America

Vol. 75 (2), 578-579
https://doi.org/10.1073/pnas.75.2.578

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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