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Irreducible modules over the mirror Heisenberg–Virasoro algebra
Communications in Contemporary Mathematics ( IF 1.2 ) Pub Date : 2021-03-16 , DOI: 10.1142/s0219199721500267
Dong Liu 1, 2 , Yufeng Pei 3 , Limeng Xia 4 , Kaiming Zhao 5, 6
Affiliation  

In this paper, we study irreducible modules over the mirror Heisenberg–Virasoro algebra 𝔇, which is the semi-direct product of the Virasoro algebra and the twisted Heisenberg algebra. We classify all Harish-Chandra modules over 𝔇, i.e. irreducible modules with finite-dimensional weight spaces. Every such module is either an irreducible highest or an irreducible lowest weight module, or an irreducible module of the intermediate series. Furthermore, we use a twisted version of Feigin–Fuchs construction of the Virasoro algebra to establish the simplicity criterion for Verma modules and obtain a classification of unitary irreducible highest weight modules over 𝔇. Finally, we determine all irreducible restricted 𝔇-modules of level zero.

中文翻译:

镜像上的不可约模 Heisenberg–Virasoro 代数

在本文中,我们研究了镜像 Heisenberg-Virasoro 代数上的不可约模𝔇,它是 Virasoro 代数和扭曲 Heisenberg 代数的半直积。我们将所有 Harish-Chandra 模块分类为𝔇,即具有有限维权空间的不可约模块。每一个这样的模要么是一个不可约最高或一个不可约最低权模,要么是一个中间级数的不可约模。此外,我们使用 Virasoro 代数的 Feigin-Fuchs 构造的扭曲版本来建立 Verma 模块的简单性标准,并获得酉不可约最高权重模块的分类𝔇. 最后,我们确定所有不可约受限的𝔇- 零级模块。
更新日期:2021-03-16
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