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

Michael Wheeler
University of Melbourne

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 https://arxiv.org/abs/2310.03527 with Jimmy He.

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