EVENT DETAILS AND ABSTRACT

Title: Bifundamental Baxter Operators
Speaker: Gus Schrader
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Abstract:

The Hamiltonians of the GL(n) open q-difference Toda lattice as well as their eigenfunctions, the q-Whittaker functions, can be neatly described by means of the system's Baxter operator. The fact that the Baxter operator acts diagonally in the basis of Whittaker functions can be regarded as a q-deformed, continuous analog of the generating function of all Pieri rules for Schur functions. In joint work with with Alexander Shapiro we introduce a kind of GL(n) x GL(m)-generalization of this Baxter operator, such that the original Baxter operator corresponds to the case m=1. These new operators can be realized as quantum cluster transformations, and govern the cluster structure on K-theoretic Coulomb branches of 3d N=4 gauge theories with bifundamental matter. This perspective leads to a categorification of the GL(n) x GL(m) Baxter operators in which cluster mutations are promoted to exact triangles in the derived category of coherent sheaves on a convolution variety.