Séminaire Lotharingien de Combinatoire, 91B.100 (2024), 12 pp.

Timothy C. Miller

Vertex Models for The Product of a Schur and Demazure Polynomial

Abstract. The product of a Schur polynomial and Demazure atom or character expands positively in Demazure atoms or characters, respectively. The structure coefficients in these expansions have known combinatorial rules in terms of skyline tableaux. We develop alternative rules using the theory of integrable vertex models, inspired by a technique introduced by Zinn-Justin. We apply this method to coloured vertex models for atoms and characters obtained from Borodin and Wheeler's models for non-symmetric Macdonald polynomials. The structure coefficients are then obtained as partition functions of vertex models that are compatible with both Schur (uncoloured) and Demazure (coloured) vertex models.

Received: November 15, 2023. Accepted: February 15, 2024. Final version: April 1, 2024.

The following versions are available: