engleski

Application of VOA to representation theory of W(2,2)-algebra and the twisted Heisenberg-Virasoro algebra

In this talk we discuss weight representations of two Virasoro-like algebras: the $W$-algebra $W(2, 2)$ and the twisted Heisenberg- Virasoro algebra at level zero $\mathcal{;H};$. We present the structure of Verma modules and formulas for singular and cosingular vectors in these algebras. These formulas are crucial for proving irreducibility of tensor products of irreducible module from intermediate series and irreducible highest weight module. Throughout the talk we see an interesting interplay with theory of VOA. Using vertex-algebraic methods we construct singular vectors in certain Verma modules over $\mathcal{;H};$. On the other hand, tensor product modules are closely related to fusion rules for irreducible $\mathcal{;H};$-modules. Finally, we give a nontrivial homomorphism between vertex-algebras $W(2, 2)$ and $\mathcal{;H};$. As a consequence, highest weight $\mathcal{;H};$- modules are also $W(2, 2)$-modules. Part of the talk is based on a recent joint work with Dražen Adamović.

Virasoro, highest weight modules, intertwining operators

nije evidentirano