Level 2 standard modules for $A^{(2)}_{9}$ and partition conditions of Kanade-Russell

TL;DR

This paper constructs explicit generators for level 2 standard modules of type A^{(2)}_{odd} and provides a Lie theoretic interpretation of Rogers-Ramanujan type identities related to A^{(2)}_{9}.

Contribution

It introduces Z-monomial generators for vacuum spaces of certain modules and interprets Rogers-Ramanujan identities within a Lie algebra framework.

Findings

Explicit Z-monomial generators for vacuum spaces.

Lie theoretic interpretation of Rogers-Ramanujan identities.

Connection to Kanade-Russell conjectures.

Abstract

We give $Z$-monomial generators for the vacuum spaces of certain level 2 standard modules of type $A^{(2)}_{\textrm{odd}}$ with indices running over integer partitions. In particular, we give a Lie theoretic interpretation of the Rogers-Ramanujan type identities of type $A^{(2)}_{9}$, which were conjectured by Kanade-Russell, and proven by Bringmann et al. and Rosengren.