Differential equations in vertex algebras and simple modules for the Lie algebra of vector fields on a torus

被引：28

作者：

Billig, Yuly ^{[1
]}

Molev, Alexander ^{[2
]}

Zhang, Ruibin ^{[2
]}

机构：

[1] Carleton Univ, Sch Math & Stat, Ottawa, ON K1S 5B6, Canada

[2] Univ Sydney, Sch Math & Stat, Sydney, NSW 2006, Australia

来源：

ADVANCES IN MATHEMATICS | 2008年 / 218卷 / 06期

基金：

澳大利亚研究理事会;

关键词：

Lie algebra of vector fields; vertex algebras; generalized Verma modules;

D O I：

10.1016/j.aim.2008.03.026

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We study irreducible representations for the Lie algebra of vector fields on a 2-dimensional torus constructed using the generalized Verma modules. We show that for a certain choice of parameters these representations remain irreducible when restricted to a loop subalgebra in the Lie algebra of vector fields. We prove this result by studying vertex algebras associated with the Lie algebra of vector fields on a torus and solving non-commutative differential equations that we derive using the vertex algebra technique. (C) 2008 Elsevier Inc. All rights reserved.

引用

页码：1972 / 2004

页数：33