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

In this article, a large class of simple modules over the Schrödinger-Virasoro algebra 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 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.