Presentations of Principal Subspaces of Higher Level Standard $A_2^{(2)}$-Modules

TL;DR

This paper investigates the structure of principal subspaces in higher level standard modules of the affine algebra $A_2^{(2)}$, providing explicit presentations and extending previous level one results.

Contribution

It introduces new presentations for principal subspaces of higher level $A_2^{(2)}$-modules, expanding the understanding beyond the previously studied level one case.

Findings

Established natural presentations of principal subspaces.

Extended earlier work to higher level modules.

Provided descriptions of related subspaces.

Abstract

We study the principal subspaces of higher level standard $A_2^{(2)}$-modules, extending earlier work in the level one case, by Calinescu, Lepowsky, and Milas. We prove natural presentations of principal subspaces and also of certain related spaces.