A family of new simple modules over the Schrödinger-Virasoro algebra

Abstract

In this article, a large class of simple modules over the Schrödinger-Virasoro algebra $\mathcal{G}$ are constructed, which include highest weight modules and Whittaker modules. These modules are determined by the simple modules over the finite-dimensional quotient algebras of some subalgebras. Moreover, we show that all simple modules of $\mathcal{G}$ with locally finite actions of elements in a certain positive part belong to this class of simple modules. Similarly, a large class of simple modules over the $W$-algebra $W(2,2)$ are constructed.

References in corpus (3)

• The Schrödinger-Virasoro Lie group and algebra: from geometry to representation theory
• Whittaker modules for the Schrödinger-Virasoro algebra
• Whittaker Modules For The W-algebra W(2,2)