Classification of Irreducible Weight Modules with a Finite.dimensional Weight Space over Twisted Heisenberg.Virasoro Algebra

We show that the support of an irreducible weight module over the twisted Heisenberg. Virasoro algebra, which has 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 corollary, we obtain that every irreducible weight module over the twisted Heisenberg.Virasoro algebra, having a nontrivial finite.dimensional weight space, is a Harish.Chandra module (and hence is either an irreducible highest or lowest weight module or an irreducible module from the intermediate series).