Unitary modules for the twisted Heisenberg-Virasoro algebra

TL;DR

This paper classifies the conjugate-linear anti-involutions and unitary irreducible modules of the intermediate series over the twisted Heisenberg-Virasoro algebra, providing a complete description of their structure.

Contribution

It introduces a classification of all unitary irreducible modules of the intermediate series over the twisted Heisenberg-Virasoro algebra, identifying their explicit form.

Findings

All unitary irreducible modules are of the form _{a,b,c}

Parameters are constrained to specific real and complex sets

Complete classification of conjugate-linear anti-involutions provided

Abstract

In this paper, the conjugate-linear anti-involutions and the unitary irreducible modules of the intermediate series over the twisted Heisenberg-Virasoro algebra are classified respectively. We prove that any unitary irreducible module of the intermediate series over the twisted Heisenberg-Virasoro algebra is of the form $\mathcal{A}_{a,b,c}$ for $a\in \mathbb{R}, b\in 1/2+\sqrt{-1}\mathbb{R}, c\in \mathbb{C}.$