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Non-injective homomorphisms between certain Verma modules

We introduce the N=1 super Heisenberg-Virasoro algebra at level zero and present its representations. By studying Fock spaces we calculate characters of all irreducible highest weight modules. As a notable difference from classical (non-super) case, the maximal submodules in some highest weight modules are generated by a subsingular vector. In these cases there exist non-injective homomorphisms between the Verma modules. We use screening operators which appear in study of certain logarithmic vertex operator algebras and obtain explicit formulas for singular and subsingular vectors. This is a joint work with D. Adamović and B. Jandrić.

vertex algebras, Heisenberg-Virasoro superalgebra, intertwining operators, screening operator

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