On the structure of Verma modules over the W-algebra W(2,2)

Abstract

In this paper, we describe the structure of Verma modules over the W-algebra W(2,2). We show that either a Verma module over W(2,2) is irreducible or its maximal submodule is cyclic.

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

“…In this section we assume 2h W + p 2 −1 12 c = 0 for some p ∈ N. Some results of this section are similar to those presented in [10] and motivated by [5]. However, since W 0 does not act semisimply in general (unlike to I 0 in the Heisenberg-Virasoro algebra), submodules generated by some singular vectors in Verma modules are not isomorphic to Verma modules so the maximal submodule J(c, h, h W ) is not necessarily cyclic on a singular vector.…”

Verma modules over deformed generalized Heisenberg-Virasoro algebras

“…Inspired by these algebras, Xu [14] introduced deformed generalized Heisenberg-Virasoro algebras g(G, λ), where λ = −1 is a deformation parameter and G is an additive subgroup of C such that G is free of rank ν if λ = −2. We also mention that the algebra g(G, 1) is a high rank generalization of the W -algebra W (2, 2), which was first introduced in [15] and extensively studied by others, for example [3,6,7].…”

θ-Unitary representations for theW-algebraW(2,2)

“…In Refs. [8,22], the Verma modules and the Whittaker modules for W(2,2) are studied, respectively. In Ref.…”