Affine Lie algebra representations induced from Whittaker modules

Cardoso, Maria Clara; Futorny, Vyacheslav

doi:10.1090/proc/16209

Affine Lie algebra representations induced from Whittaker modules
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by Maria Clara Cardoso and Vyacheslav Futorny

Proc. Amer. Math. Soc. 151 (2023), 1041-1053

DOI: https://doi.org/10.1090/proc/16209

Published electronically: December 21, 2022

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Abstract:

We use induction from parabolic subalgebras with infinite-dimensional Levi factor to construct new families of irreducible representations for arbitrary affine Kac-Moody algebras. Our first construction defines a functor from the category of Whittaker modules over the Levi factor of a parabolic subalgebra to the category of modules over the affine Lie algebra. The second functor sends tensor products of a module over the affine part of the Levi factor (in particular any weight module) and of a Whittaker module over the complement Heisenberg subalgebra to the affine Lie algebra modules. Both functors preserve irreducibility when the central charge is nonzero.

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