Tensor product weight modules for the mirror-twisted Heisenberg-Virasoro algebra

TL;DR

This paper classifies irreducible weight modules with infinite-dimensional weight spaces over the mirror-twisted Heisenberg-Virasoro algebra, introducing new modules via tensor products and analyzing their isomorphism classes and submodules.

Contribution

It provides necessary and sufficient conditions for tensor products of certain modules to be irreducible, leading to new irreducible modules over the algebra.

Findings

Characterization of irreducibility conditions for tensor products

Construction of new irreducible weight modules

Criteria for module isomorphism and submodule structure

Abstract

In this paper, we study irreducible weight modules with infinite dimensional weight spaces over the mirror-twisted Heisenberg-Virasoro algebra $\mathcal{D}$. More precisely, the necessary and sufficient conditions for the tensor products of irreducible highest weight modules and irreducible modules of intermediates series over $\mathcal{D}$ to be irreducible are determined by using "shifting technique". This leads to a family of new irreducible weight modules over $\mathcal{D}$. Then we obtain that any two such tensor products are isomorphic if and only if the corresponding highest weight modules and modules of intermediate series are isomorphic respectively. Also we discuss submodules of the tensor product module when it is not irreducible.