Andrews-Gordon type series for the level 5 and 7 standard modules of the affine Lie algebra $A^{(2)}_2$

TL;DR

This paper derives Andrews-Gordon type series for principal characters of certain level 5 and 7 modules of the affine Lie algebra A^{(2)}_2, and proposes conjectural series for some level 2 modules of A^{(2)}_{13}.

Contribution

It provides explicit series representations for characters of specific modules of affine Lie algebras, extending known formulas and proposing new conjectural series.

Findings

Series for level 5 and 7 modules of A^{(2)}_2 are established.

Conjectural series for some level 2 modules of A^{(2)}_{13} are proposed.

New formulas extend the understanding of affine Lie algebra characters.

Abstract

We give Andrews-Gordon type series for the principal characters of the level 5 and 7 standard modules of the affine Lie algebra $A^{(2)}_{2}$. We also give conjectural series for some level 2 modules of $A^{(2)}_{13}$.