Simple Virasoro modules which are locally finite over a positive part

被引：79

作者：

Mazorchuk, Volodymyr ^{[1
]}

Zhao, Kaiming ^{[2
,3
]}

机构：

[1] Uppsala Univ, Dept Math, S-75106 Uppsala, Sweden

[2] Wilfrid Laurier Univ, Dept Math, Waterloo, ON N2L 3C5, Canada

[3] Hebei Normal Teachers Univ, Coll Math & Informat Sci, Shijiazhuang 050016, Hebei, Peoples R China

来源：

SELECTA MATHEMATICA-NEW SERIES | 2014年 / 20卷 / 03期

基金：

瑞典研究理事会; 加拿大自然科学与工程研究理事会;

关键词：

Virasoro algebra; Simple module; Whittaker module; LIE-ALGEBRA SL(2); IRREDUCIBLE REPRESENTATIONS; CLASSIFICATION;

D O I：

10.1007/s00029-013-0140-8

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We propose a very general construction of simple Virasoro modules generalizing and including both highest weight and Whittaker modules. This construction enables us to classify all simple Virasoro modules that are locally finite over a positive part. To obtain those irreducible Virasoro modules, we use simple modules over a family of finite dimensional solvable Lie algebras. For one of these algebras, all simple modules are classified by R. Block and we extend this classification to the next member of the family. As a result, we recover many known but also construct a lot of new simple Virasoro modules. We also propose a revision of the setup for study of Whittaker modules.

引用

页码：839 / 854

页数：16

共 25 条

[1]

[Anonymous], 1983, Funktsional. Anal. i Prilozhen.

[2] ALGEBRAICALLY IRREDUCIBLE REPRESENTATIONS OF LIE-ALGEBRA SL(2) [J].