Classification of simple strong Harish-Chandra $W(m,n)$-modules

Yuly Billig; Vyacheslav Futorny; Kenji Iohara; Iryna Kashuba

Classification of simple strong Harish-Chandra $W(m,n)$-modules

Representation Theory 2020-06-16 v2

Authors: Yuly Billig , Vyacheslav Futorny , Kenji Iohara , Iryna Kashuba

Abstract

We classify all simple strong Harish-Chandra modules for the Lie superalgebra $W(m,n)$ . We show that every such module is either strongly cuspidal or a module of the highest weight type. We construct tensor modules for $W(m,n)$ , which are parametrized by simple finite-dimensional $gl(m,n)$ -modules and show that every simple strongly cuspidal $W(m,n)$ -module is a quotient of a tensor module. Finally, we realize modules of the highest weight type as simple quotients of the generalized Verma modules induced from tensor modules for $W(m-1,n)$ .

Keywords

lie algebras and modules highest weight modules modular forms

Cite

@article{arxiv.2006.05618,
  title  = {Classification of simple strong Harish-Chandra $W(m,n)$-modules},
  author = {Yuly Billig and Vyacheslav Futorny and Kenji Iohara and Iryna Kashuba},
  journal= {arXiv preprint arXiv:2006.05618},
  year   = {2020}
}

Comments

After this paper was completed, we learned about a recent preprint by Yaohui Xu and Rencai Lu, arXiv:2001.04089 [math.RT], where the same results were obtained

Classification of simple strong Harish-Chandra $W(m,n)$-modules

Abstract

Keywords

Cite

Comments

Related papers