engleski

Vertex algebras and combinatorial identities

In 1980's J. Lepowsky and R. Wilson gave a Lie-theoretic interpretation of Rogers-Ramanujan identities in terms of level 3 representations of affine Lie algebra sl(2, C)~. When applied to other representations and affine Lie algebras, Lepowsky-Wilson's approach yielded series of other combinatorial identities of Rogers-Ramanujan type. At about the same time R. Baxter rediscovered Rogers-Ramanujan identities in the context of statistical mechanics. The work of R. Baxter initiated another line of research which yielded numerous combinatorial and analytic generalizations of Rogers-Ramanujan identities. In this note I'll describe some ideas and results related to Lepowsky-Wilson's approach and indicate the connections with some results in combinatorics and statistical physics.

vertex operator algebras; affine Lie algebras; Rogers-Ramanujan identities

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