Subsingular vectors in Verma modules, and tensor product of weight modules over the twisted Heisenberg-Virasoro algebra and W(2,2) algebra

We show that subsingular vectors may exist in Verma modules over W(2, 2), and present the subquotient structure of these modules. We prove conditions for irreducibility of the tensor product of intermediate series module with a highest weight module. Relation to intertwining operators over vertex operator algebra associated with W(2, 2) is discussed. Also, we study the tensor product of intermediate series and a highest weight module over the twisted Heisenberg-Virasoro algebra, and present series of irreducible modules with infinite-dimensional weight spaces. (C) 2013 AIP Publishing LLC.