Naslov
On the representation theory of affine vertex algebras and W-algebras

Autori
Adamović, Dražen

Vrsta, podvrsta i kategorija rada
Sažeci sa skupova, sažetak, znanstveni

Skup
6th Croatian Mathematical Congress

Mjesto i datum
Zagreb, Hrvatska, 14.06.2016. - 17.06.2016

Vrsta sudjelovanja
Plenarno

Vrsta recenzije
Međunarodna recenzija

Ključne riječi
affine vertex algebras ; W-algebras ; logarithmic vertex algebras ; Whittaker modules ; conformal embeddings

Sažetak
In the first part of the talk we shall briefly review development and main results in the representation theory of affine vertex algebras and W–algebras obtained in the last few years. We shall discuss problems related with rationality, C_2–cofiniteness, classification of irreducible modules and relations with quantum groups. Next we shall present our main results in this direction. A particular emphasis will be put on the following topics: Representation theory of vertex algebras appearing in logarithmic conformal field theory. We shall review some results obtained on triplet vertex algebras from joint papers with A. Milas. These results gave one of the first examples of non- rational vertex algebras having finitely many irreducible modules. Classification of irreducible Wakimoto and Whittaker modules for affine vertex algebras. Explicit realizations of superconformal vertex algebras and W –algebras and their applications in the theory of conformal embeddings.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

POVEZANOST RADA