Classification of Irreducible Weight Modules with a Finite-dimensional Weight Space over the Twisted Schr\"{o}dinger-Virasoro Lie algebra

Abstract

It is shown that the support of an irreducible weight module over the Schr\"{o}dinger-Virasoro Lie algebra with an infinite-dimensional weight space, coincides with the weight lattice and that all nontrivial weight spaces of such a module are infinite-dimensional. As a side-product, it is obtained that every simple weight module over the Schr\"{o}dinger-Virasoro Lie algebra with a nontrivial finite-dimensional weight space, is a Harish-Chandra module.