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Zbl 0973.11090
Berkovich, Alexander; McCoy, Barry M.
Rogers-Ramanujan identities: A century of progress from mathematics to physics. (English)
[J] Doc. Math., J. DMV Extra Vol. ICM Berlin 1998, Vol. III, 163-172 (1998). ISSN 1431-0635; ISSN 1431-0643/e

Summary: In this talk we present the discoveries made in the theory of Rogers-Ramanujan identities in the last five years which have been made because of the interchange of ideas between mathematics and physics. We find that not only does every minimal representation $M(p,p')$ of the Virasoro algebra lead to a Rogers-Ramanujan identity but that different coset constructions lead to different identities. These coset constructions are related to the different integrable perturbations of the conformal field theory. We focus here in particular on the Rogers-Ramanujan identities of the $M(p,p')$ models for the perturbations $\phi_{1,3},\sim\phi_{2,1},\sim\phi_{1,2}$ and $\phi_{1,5}.$

MSC 2000:: *11P99 Additive number theory
05A19 Combinatorial identities
82B20 Lattice systems
17B67 Kac-Moody algebras
81T40 Two-dimensional field theories, etc.

Keywords: Rogers-Ramanujan identities; lattice models; conformal field theory; affine Lie algebras

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