Lepowsky's and Wakimoto's product formulas for the affine Lie algebras Cl(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 Cl(1), Dl+1(2) and A2l(2). Lepowsky-Wakimoto's infinite periodic products appear as one side of (conjectured) Rogers-Ramanujan-type combinatorial identities for affine Lie algebras of type Cl(1).
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