Level 2 standard modules for $A_9^{(2)}$ and partition conditions of Kanade-Russell

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