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

Autori
Radobolja, Gordan

Vrsta, podvrsta i kategorija rada
Sažeci sa skupova, neobjavljeni rad, znanstveni

Skup
Infinite Dimensional Lie Theory and its Applications

Mjesto i datum
Allahābād, Indija, 15.12.2014. - 20.12.2014

Vrsta sudjelovanja
Pozvano predavanje

Vrsta recenzije
Nije recenziran

Ključne riječi
Virasoro, highest weight modules, intertwining operators

Sažetak
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.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

POVEZANOST RADA