Free field realization of the twisted Heisenberg-Virasoro algebra at level zero and its applications
arXiv:1405.1707 · doi:10.1016/j.jpaa.2015.02.019
Abstract
We investigate the free fields realization of the twisted Heisenberg-Virasoro algebra at level zero. We completely describe the structure of the associated Fock representations. Using vertex-algebraic methods and screening operators we construct singular vectors in certain Verma modules as Schur polynomials. We completely solve the irreducibility problem for tensor product of irreducible highest weight modules with intermediate series. We also determine the fusion rules for an interesting subcategory of -modules. Finally, as an application we present a free field realization of the -algebra and interpret the -singular vectors as -singular vectors in Verma modules.
To appear in Journal of Pure and Applied Algebra, 24 pages
References in corpus (9)
- Logarithmic tensor product theory for generalized modules for a conformal vertex algebra, Part I
- Logarithmic tensor category theory, VIII: Braided tensor category structure on categories of generalized modules for a conformal vertex algebra
- Logarithmic tensor category theory, VII: Convergence and extension properties and applications to expansion for intertwining maps
- Tensor product weight modules over the Virasoro algebra
- Subsingular vectors in Verma modules, and tensor product modules over the twisted Heisenberg-Virasoro algebra and W(2,2) algebra
- On W-algebras associated to (2,p) minimal models and their representations
- Logarithmic tensor product theory for generalized modules for a conformal vertex algebra
- Application of vertex algebras to the structure theory of certain representations over the Virasoro algebra
- Representations of Lie algebra of vector fields on a torus and chiral de Rham complex