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 50 条
  • [21] Vertex operator algebras and irreducibility of certain modules for affine Lie algebras
    Adamovic, D
    MATHEMATICAL RESEARCH LETTERS, 1997, 4 (06) : 809 - 821
  • [22] DOUBLE AFFINE LIE ALGEBRAS AND FINITE GROUPS
    Guay, Nicolas
    Hernandez, David
    Loktev, Sergey
    PACIFIC JOURNAL OF MATHEMATICS, 2009, 243 (01) : 1 - 41
  • [23] Trigonometric Lie algebras, affine Kac-Moody Lie algebras, and equivariant quasi modules for vertex algebras
    Guo, Hongyan
    Li, Haisheng
    Tan, Shaobin
    Wang, Qing
    JOURNAL OF ALGEBRA, 2023, 636 : 42 - 74
  • [24] Simple modules for twisted Hamiltonian extended affine Lie algebras
    Tantubay, Santanu
    Chakraborty, Priyanshu
    Batra, Punita
    LINEAR ALGEBRA AND ITS APPLICATIONS, 2024, 696 : 29 - 45
  • [25] Dimensions of Demazure modules for rank two affine Lie algebras
    Sanderson, YB
    COMPOSITIO MATHEMATICA, 1996, 101 (02) : 115 - 131
  • [26] Gauge Modules for the Lie Algebras of Vector Fields on Affine Varieties
    Yuly Billig
    Jonathan Nilsson
    André Zaidan
    Algebras and Representation Theory, 2021, 24 : 1141 - 1153
  • [27] Gauge Modules for the Lie Algebras of Vector Fields on Affine Varieties
    Billig, Yuly
    Nilsson, Jonathan
    Zaidan, Andre
    ALGEBRAS AND REPRESENTATION THEORY, 2021, 24 (05) : 1141 - 1153
  • [28] Verma-type modules for quantum affine Lie algebras
    Futorny, VM
    Grishkov, AN
    Melville, DJ
    ALGEBRAS AND REPRESENTATION THEORY, 2005, 8 (01) : 99 - 125
  • [29] Braided Tensor Categories of Admissible Modules for Affine Lie Algebras
    Thomas Creutzig
    Yi-Zhi Huang
    Jinwei Yang
    Communications in Mathematical Physics, 2018, 362 : 827 - 854
  • [30] Verma-Type Modules for Quantum Affine Lie Algebras
    Vyacheslav M. Futorny
    Alexander N. Grishkov
    Duncan J. Melville
    Algebras and Representation Theory, 2005, 8 : 99 - 125
12345