Naslov
On indecomposable and logarithmic modules for affine vertex operator algebras

Autori
Adamović, Dražen

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

Skup
Vertex operator algebras, number theory, and related topics

Mjesto i datum
Sacramento (CA), Sjedinjene Američke Države, 11.06.2018. - 15.06.2018

Vrsta sudjelovanja
Pozvano predavanje

Vrsta recenzije
Međunarodna recenzija

Ključne riječi
Affine vertex algebras ; complete reducibility, logarithmic modules

Sažetak
Admissible affine vertex operator algebras $V_{; ; k}; ; (\mathfrak g)$ are semi-simple in the category $\mathcal O$. In this talk, we shall first present a complete reducibility result for a large class of simple affine vertex operator algebras $V_{; ; k}; ; (\mathfrak g)$ at non-admissible levels (joint work with Kac, Moseneder-Frajria, Papi and Perse). Then we shall consider $V_{; ; k}; ; (\mathfrak g)$--modules outside of the category $\mathcal O$. Logarithmic modules appear in the non-split extension of certain weight modules. Although $V_{; ; k}; ; (\mathfrak g)$--modules are modules for the affine Lie algebras, it is difficult to construct indecomposable and logarithmic modules using concepts from the representation theory of Lie algebras. We will show how these modules can be explicitly constructed using vertex-algebraic techniques. We will also show that certain Whittaker modules are also weak $V_{; ; k}; ; (\mathfrak g)$--modules.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

POVEZANOST RADA