Michael Wheeler - A vertex model proof of a correspondence due to Imamura--Mucciconi--Sasamoto

Recorded 24 May 2024. Michael Wheeler of the University of Melbourne presents "A vertex model proof of a correspondence due to Imamura--Mucciconi--Sasamoto" at IPAM's Vertex Models: Algebraic and Probabilistic Aspects of Universality Workshop.
Abstract: The q-Whittaker polynomials are a one-parameter generalization of Schur polynomials, with many nice combinatorial properties. It has been known for quite a few years that they admit two different formulas as partition functions of vertex models: one as a partition function of coloured lattice paths on a cylinder, and the other as a partition function of colourless lattice paths in the plane.
In this talk I will explain where this correspondence comes from, and how when it is specialized appropriately, yields a vertex model proof of a match between q-Whittaker and periodic Schur measures, originally obtained by Imamura, Mucciconi and Sasamoto.
This is based on a joint work arxiv.org/abs/2310.03527 with Jimmy He.
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