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

Abstract: We give $Z$-monomial generators for the vacuum spaces of certain level 2 standard modules of type $A^{(2)}_{\textrm{odd}}$ 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.