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

Autor:	Billig, Yuly, Futorny, Vyacheslav, Iohara, Kenji, Kashuba, Iryna
Rok vydání:	2020
Předmět:	Mathematics - Representation Theory 17B10 17B66 17B68
Druh dokumentu:	Working Paper
Popis:	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 $W(m-1,n)$. Comment: 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
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2006.05618 Zobrazit plný text záznamu View this record from Arxiv