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Crystal limit and Baxter's Q-operator: a combinatorial construction of WZNW fusion rings

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Discrete Integrable Systems

Considering the crystal limit of the modular XXZ spin-chain I will show that one arrives at a purely combinatorial construction of the fusion ring (also known as Verlinde algebra) of su(n) Wess-Zumino-Novikov-Witten (WZNW) conformal field theory. The transfer matrix and Baxter’s Q-operator have a well defined meaning in this limit: they correspond to symmetric polynomials in non-commutative variables which are related to Kashiwara’s crystal operators.

This talk is part of the Isaac Newton Institute Seminar Series series.

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