Unitary representations for the Schrödinger-Virasoro Lie algebra

Abstract

In this paper, conjugate-linear anti-involutions and unitary Harish-Chandra modules over the Schrödinger-Virasoro algebra are studied. It is proved that there are only two classes conjugate-linear anti-involutions over the Schrödinger-Virasoro algebra. The main result of this paper is that a unitary Harish-Chandra module over the Schrödinger-Virasoro algebra is simply a unitary Harish-Chandra module over the Virasoro algebra.