Unitary modules for the twisted Heisenberg-Virasoro algebra

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 $a\in \mathbb{R},b\in 1/2+\sqrt{-1}\mathbb{R},c\in \mathbb{C}.$