Open AccessLie algebras and classical partition identities
Author(s) -
James Lepowsky,
Stephen C. Milne
Publication year - 1978
Publication title -
proceedings of the national academy of sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 5.011
H-Index - 771
eISSN - 1091-6490
pISSN - 0027-8424
DOI - 10.1073/pnas.75.2.578
Subject(s) - mathematics , cartan matrix , partition (number theory) , pure mathematics , lie algebra , euclidean geometry , algebra over a field , ramanujan's sum , kac–moody algebra , weight , adjoint representation of a lie algebra , combinatorics , geometry
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.
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