Young wall model for $A_2^{(2)}$-type adjoint crystals

TL;DR

This paper develops a Young wall model for higher level $A_2^{(2)}$-type adjoint crystals, linking combinatorial structures with affine crystal representations.

Contribution

It introduces a novel Young wall construction for $A_2^{(2)}$-type crystals and demonstrates their realization of highest weight crystals.

Findings

Young wall model successfully represents $A_2^{(2)}$-type crystals

Reduced Young walls realize highest weight crystals $B()$ and $B()

Connection established with affine energy functions

Abstract

We construct a Young wall model for higher level $A_2^{(2)}$-type adjoint crystals. The Young walls and reduced Young walls are defined in connection with affin energy function. We prove that the affine crystal consisiting of reduced Young walls provides a realization of highest weight crystals $B(\lambda)$ and $B(\infty)$.