Classification of Simple Strong Harish-Chandra Modules Over the Lie Superalgebra of Vector Fields on Cm|n

被引：0

作者：

Cai, Yan-an ^{[1
]}

Lu, Rencai ^{[1
]}

Xue, Yaohui ^{[1
,2
]}

机构：

[1] Soochow Univ, Dept Math, Suzhou, Peoples R China

[2] Nantong Univ, Sch Math & Stat, Nantong, Peoples R China

来源：

TRANSFORMATION GROUPS | 2025年

基金：

中国国家自然科学基金;

关键词：

Lie superalgebra of vector fields; Simple weight modules; Strong Harish-Chandra modules; SIMPLE WEIGHT MODULES; CARTAN TYPE; DIFFEOMORPHISMS; REPRESENTATIONS; ALGEBRAS;

D O I：

10.1007/s00031-025-09915-1

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we classify simple strong Harish-Chandra modules over the Lie superalgebra-Wm, n of vector fields on Cm|n. Any such module is the unique simple submodule of some tensor module F(P, V) for a simple weight module P over the Weyl superalgebra Km, n and a simple weight module V over the general linear superalgebra glm,n.

引用

页数：22

共 29 条

[1]

Bernstein IN., 1983, Selecta Math. Soviet, V3, P63

[2]

Billig Y., arXiv

[3] Classification of simple cuspidal modules for solenoidal Lie algebras [J].