Admissible representations of simple affine vertex algebras

Futorny，Vyacheslav1,2; Morales，Oscar2; Křižka，Libor2

2023-08-15

10.1016/j.jalgebra.2023.03.010

Journal of Algebra   Impact Factor & Quartile

0021-8693

1090-266X

We provide an explicit combinatorial description of highest weights of simple highest weight modules over the simple affine vertex algebra L(sl) with n∈N of admissible level κ. For admissible simple highest weight modules corresponding to the principal, subregular and maximal parabolic nilpotent orbits we give a realization using the Gelfand–Tsetlin theory, which also allows us to obtain a realization of certain classes of simple admissible sl-induced modules in these orbits. In particular, simple admissible sl-induced modules are fully classified for the principal nilpotent orbit.

Affine Kac–Moody algebra Affine vertex algebra Gelfand–Tsetlin module Nilpotent orbit

SCI

English

First ; Corresponding

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior[001];Fundação de Amparo à Pesquisa do Estado do Amazonas[071/2022];Fundação de Amparo à Pesquisa do Estado de São Paulo[2018/23690-6];Conselho Nacional de Desenvolvimento Científico e Tecnológico[302884/2021-1];

WOS:000982215100001

MATHEMATICS

2-s2.0-85151322061

Scopus

1.International Center for Mathematics,SUSTech University,Shenzhen,China
2.Instituto de Matemática e Estatística,Universidade de São Paulo,São Paulo,Brazil

Futorny，Vyacheslav,Morales，Oscar,Křižka，Libor. Admissible representations of simple affine vertex algebras[J]. Journal of Algebra,2023,628:22-70.

Futorny，Vyacheslav,Morales，Oscar,&Křižka，Libor.(2023).Admissible representations of simple affine vertex algebras.Journal of Algebra,628,22-70.

Futorny，Vyacheslav,et al."Admissible representations of simple affine vertex algebras".Journal of Algebra 628(2023):22-70.