Level 2 standard modules for A9(2) and partition conditions of Kanade-Russell

Abstract

We give Z-monomial generators for the vacuum spaces of certain level 2 standard modules of type $A_{\text{odd}}^{\left(2\right)}$ with indices running over integer partitions. In particular, we give a Lie theoretic interpretation of the Rogers-Ramanujan type identities of type $A_9^{\left(2\right)}$, which were conjectured by Kanade-Russell, and proven by Bringmann et al. and Rosengren.