Work

Affine Lie algebras representations induced from Whittaker modules

Year: 2022

Type: preprint

Abstract: We use induction from parabolic subalgebras with infinite-dimensional Levi factor to construct new families of irreducible representations for arbitrary Affine Kac-Moody algebra. 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 preserves irreducibility when the central charge is nonzero.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2203.13033

Authors: Cardoso, Maria Clara, Futorny, Vyacheslav

Institutions: Southern University of Science and Technology, Universidade de São Paulo

Language: English

Topic: Algebraic structures and combinatorial models

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funder: Conselho Nacional de Desenvolvimento Científico e Tecnológico

Awards: G1413624030, G5191271473, G7026072918

OpenAlex ID: W4221139134

Cites:

Cited by: 1

Related to: 10