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Level 2 standard modules for $A^{(2)}_{9}$ and partition conditions of Kanade-Russell (2211.03652v3)
Published 7 Nov 2022 in math.RT
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.