Closed Colored Models and Demazure Crystals

TL;DR

This paper constructs solvable lattice models with partition functions as Demazure characters, establishes a crystal structure on the model states, and proves these states form a Demazure crystal, linking statistical mechanics and algebraic combinatorics.

Contribution

It introduces a novel connection between solvable lattice models and Demazure crystals, providing a new combinatorial and algebraic framework.

Findings

Partition functions correspond to Demazure characters

A crystal structure is constructed on the model states

States form a Demazure crystal

Abstract

We will construct solvable lattice models whose partition functions are Demazure characters. We will construct a crystal structure on the states of the model and prove that the states of the closed model form a Demazure crystal.