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Rogers-Ramanujan identities: A century of progress from mathematics to physics. (English) Zbl 0973.11090
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 $M\left(p,{p}^{\text{'}}\right)$ 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 $M\left(p,{p}^{\text{'}}\right)$ models for the perturbations ${\phi }_{1,3},\sim {\phi }_{2,1},\sim {\phi }_{1,2}$ and ${\phi }_{1,5}·$
##### MSC:
 11P99 Additive number theory 05A19 Combinatorial identities, bijective combinatorics 82B20 Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs 17B67 Kac-Moody (super)algebras; extended affine Lie algebras; toroidal Lie algebras 81T40 Two-dimensional field theories, conformal field theories, etc.