Vertex Algebras and Combinatorial Identities

Author: Primc M.

Source: Acta Applicandae Mathematicae, Volume 73, Numbers 1-2, August 2002 , pp. 221-238(18)

Publisher: Springer

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Abstract:

In the 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 and Wilson's approach yielded a series of other combinatorial identities of the Rogers–Ramanujan type. At about the same time, R. Baxter rediscovered Rogers–Ramanujan identities within 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, we describe some ideas and results related to Lepowsky and Wilson's approach and indicate the connections with some results in combinatorics and statistical physics.

Keywords: vertex operator algebras; affine Lie algebras; Rogers–Ramanujan identities

Language: English

Document Type: Research article

Affiliations: 1: Department of Mathematics, University of Zagreb, Zagreb, Croatia

Publication date: 2002-08-01