Modules for double affine Lie algebras

被引：0
作者：
Naihuan Jing
Chunhua Wang
机构：
[1] South China University of Technology,School of Mathematics
[2] North Carolina State University,Department of Mathematics
来源：
Frontiers of Mathematics in China | 2016年 / 11卷
关键词：
Double affine Lie algebra; Verma module; irreducibility; Weyl module; 17B67; 17B10; 17B65;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
Imaginary Verma modules, parabolic imaginary Verma modules, and Verma modules at level zero for double affine Lie algebras are constructed using three different triangular decompositions. Their relations are investigated, and several results are generalized from the affine Lie algebras. In particular, imaginary highest weight modules, integrable modules, and irreducibility criterion are also studied.
引用
收藏
页码：89 / 108
页数：19
相关论文
共 17 条
  • [1] Chang X(2011)A class of irreducible integrable modules for the extended baby TKK algebra. Pacific J Math 252 293-312
  • [2] Tan S(2011)Representations of affine and toroidal Lie algebras. Geometric Representation Theory and Extended Affine Lie Algebras. Fields Inst Commun 59 169-197
  • [3] Chari V(2001)Weyl modules for classical and quantum affine algebras. Represent Theory 5 191-223
  • [4] Chari V(2003)Imaginary Verma modules for the extended affine Lie algebra sl2(Cq). Comm Algebra 31 289-308
  • [5] Pressley A(1994)Imaginary Verma modules for affine Lie algebras. Canad Math Bull 37 213-218
  • [6] Dokuchaev M F L V(1999)Verma type modules for toroidal Lie algebras. Comm Algebra 27 3979-3991
  • [7] Futorny V(1978)The arithmetic theory of loop algebras. J Algebra 53 480-551
  • [8] Futorny V(1992)Toroidal Weyl groups. Nova J Algebra Geom 1 317-337
  • [9] Futorny V(2001)Classification of irreducible integrable modules for multi-loop algebras with finite dimensional weight spaces J Algebra 246 215-225
  • [10] Kashuba I(2004)Classification of irreducible integrable modules for toroidal Lie algebras with finite dimensional weight spaces J Algebra 277 318-348
12