Abstract: Lepowsky and Wilson initiated the approach to combinatorial Rogers-Ramanujan type identities via vertex operator constructions of standard (i.e., integrable highest weight) representations of affine Kac-Moody Lie algebras. Meurman and Primc developed further this approach for by using vertex operator algebras and Verma modules. In this paper, we use the same method […]
Abstract: Building on work of the first and last author, we prove that an embedding of simple affine vertex algebras , corresponding to an embedding of a maximal equal rank reductive subalgebra into a simple Lie algebra , is conformal if and only if the corresponding central charges are equal. […]
We prove the irreducibility of the universal non-degenerate Whittaker modules for the affine Lie algebra of type with noncritical level. These modules can become simple Whittaker modules over with the same Whittaker function and central charge. We have to modulo a central character for sl2sl2 to obtain simple degenerate Whittaker […]
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