Lepowsky's and Wakimoto's product formulas for the affine Lie algebras $C_l^{(1)}$

Abstract

In this paper, we recall Lepowsky's and Wakimoto's product character formulas formulated in a new way by using arrays of specialized weighted crystals of negative roots for affine Lie algebras of type $C_l^{(1)}$, $D_{l+1}^{(2)}$ and $A_{2l}^{(2)}$. Lepowsky-Wakimoto's infinite periodic products appear as one side of (conjectured) Rogers-Ramanujan-type combinatorial identities for affine Lie algebras of type $C_l^{(1)}$.

37 pages, 43 figures

References in corpus (1)

• The ${\mathrm{A}}_2$ Andrews-Gordon identities and cylindric partitions