engleski

Realizations of simple affine vertex algebras and decompositions in conformal embeddings

In the first part of the talk we review our recent explicit realizations of certain affine vertex algebras and discuss their applications in the representation theory. We describe a construction of logarithmic modules and Whittaker modules for admissible affine vertex algebras $V_k(sl(2))$. Next, we report on new developments in the study of conformal embeddings of affine vertex algebras (a joint project with Kac, Papi, Moseneder-Frajria, and Perse). We present new results and conjectures on decompositions in conformal embeddings by applying affine fusion rules, explicit realizations and $q$-series identities.

Affine vertex algebras ; explicit realizations ; logarithmic and Whittaker modules

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