Quasi-solvable lattice models for Sp2n and SO2n+1 Demazure atoms and characters

作     者：Buciumas, Valentin Scrimshaw, Travis 

作者机构：Univ Alberta Edmonton AB T6G 2G1 Canada Univ Queensland Sch Math & Phys St Lucia Qld 4072 Australia 

出 版 物：《FORUM OF MATHEMATICS SIGMA》 (Forum Math., Sigma)

年 卷 期：2022年第10卷

页      面：e53-e53页

核心收录：

基　　金：Australian Research Council [DP180103150, DP17010264] NSERC [RGPIN-2019-06112] endowment of the M.V. Subbarao Professorship in Number Theory Grants-in-Aid for Scientific Research [21F51028] Funding Source: KAKEN 

摘      要：We construct coloured lattice models whose partition functions represent symplectic and odd orthogonal Demazure characters and atoms. We show that our lattice models are not solvable, but we are able to show the existence of sufficiently many solutions of the Yang-Baxter equation that allow us to compute functional equations for the corresponding partition functions. From these functional equations, we determine that the partition function of our models are the Demazure atoms and characters for the symplectic and odd orthogonal Lie groups. We coin our lattice models as quasi-solvable. We use the natural bijection of admissible states in our models with Proctor patterns to give a right key algorithm for reverse King tableaux and Sundaram tableaux.