A note on $U_q(D_4^{(3)})$ - Demazure crystals

TL;DR

This paper investigates the structure of Demazure crystals associated with the quantum affine algebra U_q(D_4^{(3)}), demonstrating a specific Weyl group sequence that yields a tensor product-like path realization with a mixing index of 1.

Contribution

It introduces a suitable Weyl group sequence for Demazure crystals of U_q(D_4^{(3)}), revealing a tensor product-like structure with mixing index 1.

Findings

Existence of a Weyl group sequence for Demazure crystals

Path realizations exhibit tensor product-like structure

Mixing index for the structure is 1

Abstract

We show that there exists a suitable sequence $\{w^{(k)}\}_{k \ge 0}$ of Weyl group elements for the perfect crystal $B = B^{1,3l}$ such that the path realizations of the Demazure crystals $B_{w^{(k)}}(l\Lambda_2)$ for the quantum affine algebra $U_q(D_4^{(3)})$ have tensor product like structure with mixing index $\kappa =1$.