Cluster structure on spherical DAHA: how and why

Alexander Shapiro (University of Edinburgh)

Tuesday 12th November 16:00-17:00 Maths 311B

Abstract

I will attempt to explain how one can endow spherical DAHA with the structure of a quantised cluster Poisson variety, and what such a structure can be used for. In particular, we will construct an SL(2,Z)-equivariant representation of sDAHA, and construct an explicit equivalence between Toda and Ruijsenaars integrable systems. The talk will be based on joint works with Philippe Di Francesco, Rinat Kedem, Sergey Khoroshkin, and Gus Schrader.I will attempt to explain how one can endow spherical DAHA with the structure of a quantised cluster Poisson variety, and what such a structure can be used for. In particular, we will construct an SL(2,Z)-equivariant representation of sDAHA, and construct an explicit equivalence between Toda and Ruijsenaars integrable systems. The talk will be based on joint works with Philippe Di Francesco, Rinat Kedem, Sergey Khoroshkin, and Gus Schrader.

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