WHITTAKER MODULES FOR THE VIRASORO ALGEBRA

被引：88
|
作者：
Ondrus, Matthew [1 ]
Wiesner, Emilie [2 ]
机构：
[1] Weber State Univ, Dept Math, Ogden, UT 84408 USA
[2] Ithaca Coll, Dept Math, Ithaca, NY 14850 USA
来源：
JOURNAL OF ALGEBRA AND ITS APPLICATIONS | 2009年 / 8卷 / 03期
关键词：
Virasoro algebra; Whittaker modules; representations; simple modules; central characters; IRREDUCIBLE REPRESENTATIONS; SL(2);
D O I：
10.1142/S0219498809003370
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
Whittaker modules have been well studied in the setting of complex semisimple Lie algebras. Their definition can easily be generalized to certain other Lie algebras with triangular decomposition, including the Virasoro algebra. We define Whittaker modules for the Virasoro algebra and obtain analogues to several results from the classical setting, including a classification of simple Whittaker modules by central characters and composition series for general Whittaker modules.
引用
收藏
页码：363 / 377
页数：15
相关论文
共 50 条
  • [21] Whittaker modules for a Lie algebra of Block type
    Bin Wang
    Xinyun Zhu
    Frontiers of Mathematics in China, 2011, 6 : 731 - 744
  • [22] New simple Virasoro modules from Weyl algebra modules
    Li, Shujuan
    Qin, Mengyao
    Guo, Xiangqian
    JOURNAL OF ALGEBRA, 2022, 609 : 619 - 641
  • [23] GENERALIZED POLYNOMIAL MODULES OVER THE VIRASORO ALGEBRA
    Liu, Genqiang
    Zhao, Yueqiang
    PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2016, 144 (12) : 5103 - 5112
  • [24] Modules over algebras related to the Virasoro algebra
    Chen, Qiufan
    Cai, Yan-an
    INTERNATIONAL JOURNAL OF MATHEMATICS, 2015, 26 (09)
  • [25] A new family of modules over the Virasoro algebra
    Chen, Hongjia
    Guo, Xiangqian
    JOURNAL OF ALGEBRA, 2016, 457 : 73 - 105
  • [26] λ-Differential operators and λ-differential modules for the Virasoro algebra
    Liu, Xuewen
    Guo, Li
    Guo, Xiangqian
    LINEAR & MULTILINEAR ALGEBRA, 2019, 67 (07): : 1308 - 1324
  • [27] Extensions of "thickened" Verma modules of the Virasoro algebra
    Brown, KS
    JOURNAL OF ALGEBRA, 2003, 269 (01) : 160 - 188
  • [28] Simple Singular Whittaker Modules Over the Schrodinger Algebra
    Cai, Yan-an
    Zhang, Xiufu
    COMMUNICATIONS IN MATHEMATICS AND STATISTICS, 2019, 7 (04) : 475 - 483
  • [29] Simple Heisenberg-Virasoro modules from Weyl algebra modules
    Li, Shujuan
    Zhu, Junyi
    Guo, Xiangqian
    JOURNAL OF ALGEBRA, 2024, 638 : 682 - 719
  • [30] Whittaker Modules for the Insertion-Elimination Lie Algebra
    Ondrus, Matthew
    Wiesner, Emilie
    ALGEBRAS AND REPRESENTATION THEORY, 2017, 20 (04) : 843 - 856
12345