Primc, Mirko; matematični kolokvij september 2000

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Vertex operators and combinatorial identities

Mirko Primc

Univerza v Zagrebu

14. september 2000

Rogers-Ramanujan identities, first discovered by L. J. Rogers in 1894, are two analytic identities expressing certain infinite sums as infinite products. These identities were a starting point of an analytic theory further developed by S. Ramanujan, I. J. Schur, W. N. Bailey, B. Gordon, G. E. Andrews and D. Bressoud, to mention just a few, with many connections with number theory and combinatorics. In 1980's J. Lepowsky and R. Wilson gave a Lie-theoretic interpretation of Rogers-Ramanujan identities in terms of certain representations of affine Lie algebras, and, at about the same time, R. Baxter rediscovered Rogers-Ramanujan identities in the context of statistical mechanics. In this talk I'll describe some ideas and results related to Lepowsky-Wilson's approach, based on vertex operator constructions of representations of affine Kac-Moody Lie algebras, and indicate the connections with some results in statistical physics and conformal field theory, obtained by Kyoto school and Stony Brook group in 1990's.

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