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

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.

28 pages

References in corpus (1)

• Application of vertex algebras to the structure theory of certain representations over the Virasoro algebra

Cited by in corpus (8)

• Generalized oscillator representations of the twisted Heisenberg-Virasoro algebra
• Free field realization of the twisted Heisenberg-Virasoro algebra at level zero and its applications
• Two classes of non-weight modules over the twisted Heisenberg-Virasoro algebra
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• Local derivations on the Lie algebra $W(2,2)$
• The BRST quantisation of chiral BMS-like field theories
• Aspects of infinite dimensional $\ell$-super Galilean conformal algebra
• Galilean $W_3$ algebra