Generalized Verma Modules over Lie Algebras of Weyl Type

被引：1

作者：

Xin, Bin ^{[1
,2
]}

Wu, Yuezhu ^{[3
]}

机构：

[1] Univ Sci & Technol China, Dept Math, Hefei 230026, Anhui, Peoples R China

[2] Guizhou Normal Univ, Coll Math & Comp Sci, Guiyang 550001, Peoples R China

[3] Qufu Normal Univ, Dept Math, Qufu 273165, Shandong, Peoples R China

来源：

ALGEBRA COLLOQUIUM | 2009年 / 16卷 / 01期

关键词：

generalized Verma module; generalized Weyl algebra; W-infinity algebra; quasifinite; irreducibility; HIGHEST WEIGHT REPRESENTATIONS; MATRIX DIFFERENTIAL-OPERATORS; QUASIFINITE REPRESENTATIONS; CLASSIFICATION; 2-COCYCLES; FAMILY;

D O I：

10.1142/S1005386709000157

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

For a field F of characteristic 0 and an additive subgroup Gamma of F, there corresponds a Lie algebra (W) over cap(Gamma) of generalized Weyl type. Given a total order of Gamma and a weight Lambda, a generalized Verma (W) over cap(Gamma)-module M (Lambda, <) is defined. In this paper, the irreducibility of M(Lambda, <) is completely determined. It is also proved that an irreducible highest weight module over the W-infinity algebra W1+infinity is quasifinite if and only if it is a proper quotient of a Verma module.

引用

页码：131 / 142

页数：12

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