engleski

On logarithmic and Whittaker modules for affine vertex operator algebras and beyond

Simple affine vertex algebras at admissible levels are semi-simple in the category O, but beyond the category O they contain interesting categories of representations with many new research challenges. We shall first discuss the existence and explicit realization of logarithmic modules which appear as extensions of weight modules. Next natural task is to include Whittaker modules in the representation category. Although Whittaker modules are constructed using standard Lie-theoretic constructions, we will show that in order to understand the structure of affine Whittaker modules, one needs to apply vertex-algebraic techniques. We also present our explicit lattice realizations of Whittaker modules for simple VOA $L_k(sl(2))$ at arbitrary admissible level $k$, and our recent efforts to generalize this realization in higher rang cases. We will try to predict possible fusion rules and intertwining operators which include Whittaker-type modules.

Logarithmic modules ; Whittaker modules ; affine vertex algebra

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