Asian Journal of Mathematics

Volume 24 (2020)

Number 2

New irreducible tensor product modules for the Virasoro algebra

Pages: 191 – 206

DOI: https://dx.doi.org/10.4310/AJM.2020.v24.n2.a1

Authors

Xiangqian Guo (School of Mathematics and Statistics, Zhengzhou University, Zhengzhou, Henan Province, China)

Xuewen Liu (School of Mathematics and Statistics, Zhengzhou University, Zhengzhou, Henan Province, China; and School of Mathematics and Statistics, Lanzhou University, Lanzhou, Gansu Province, China)

Jing Wang (School of Mathematics and Statistics, Zhengzhou University, Zhengzhou, Henan Province, China)

Abstract

In this paper, we obtain a class of Virasoro modules by taking tensor products of the irreducible Virasoro modules $\Omega (\lambda, \alpha, h)$ defined in [CG1], with irreducible highest weight modules $V (\theta, h)$ or with irreducible Virasoro modules $\operatorname{Ind}_\theta (N)$ defined in [MZ2]. We obtain the necessary and sufficient conditions for such tensor product modules to be irreducible, and determine the necessary and sufficient conditions for two of them to be isomorphic. These modules are not isomorphic to any other known irreducible Virasoro modules.

Keywords

Virasoro algebra, tensor products, non-weight modules, irreducible modules

2010 Mathematics Subject Classification

17B10, 17B20, 17B65, 17B66, 17B68

Full Text (PDF format)

This work is partially supported by the NSF of China (Grant Nos. 11471294, 11971440), and by the Outstanding Young Talent Research Fund of Zhengzhou University (Grant 1421315071).

Received 15 March 2017

Accepted 17 May 2019

Published 8 September 2020