Non-weight modules over the mirror Heisenberg-Virasoro algebra

被引:0
|
作者
Dongfang Gao
Yao Ma
Kaiming Zhao
机构
[1] University of Science and Technology of China,School of Mathematical Sciences
[2] Northeast Normal University,School of Mathematics and Statistics
[3] Wilfrid Laurier University,Department of Mathematics
[4] Hebei Normal University,School of Mathematical Sciences
来源
Science China Mathematics | 2022年 / 65卷
关键词
mirror Heisenberg-Virasoro algebra; tensor product; Whittaker module; -free module; irreducible module; 17B10; 17B20; 17B65; 17B66; 17B68;
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学科分类号
摘要
In this paper, we study irreducible non-weight modules over the mirror Heisenberg-Virasoro algebra D\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\cal D}$$\end{document}, including Whittaker modules, U(ℂd0)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\cal U}\left( {{\mathbb{C}d_0}} \right)$$\end{document}-free modules and their tensor products. More precisely, we give the necessary and sufficient conditions for the Whittaker modules to be irreducible. We determine all the D\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\cal D}$$\end{document}-module structures on U(ℂd0)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\cal U}\left( {{\mathbb{C}d_0}} \right)$$\end{document}, and find the necessary and sufficient conditions for these modules to be irreducible. At last, we determine the necessary and sufficient conditions for the tensor products of Whittaker modules and U(ℂd0)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\cal U}\left( {{\mathbb{C}d_0}} \right)$$\end{document}-free modules to be irreducible, and obtain that any two such tensor products are isomorphic if and only if the corresponding Whittaker modules and U(ℂd0)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\cal U}\left( {{\mathbb{C}d_0}} \right)$$\end{document}-free modules are isomorphic. These lead to many new irreducible non-weight modules over D\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\cal D}$$\end{document}.
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收藏
页码:2243 / 2254
页数:11
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