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

TL;DR

This paper investigates the structure of Verma modules over W(2,2) and twisted Heisenberg-Virasoro algebra, revealing subsingular vectors, subquotient structures, and conditions for irreducibility in tensor products, with implications for vertex operator algebras.

Contribution

It introduces the existence of subsingular vectors in W(2,2) Verma modules and characterizes irreducibility conditions for tensor products involving these modules.

Findings

Subsidiary vectors exist in W(2,2) Verma modules.

Conditions for irreducibility of tensor products are established.

Constructs new irreducible modules with infinite-dimensional weight spaces.

Abstract

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