engleski

On the representation theory of affine vertex algebras at collapsing level

In the first part of the talk we recall recent results on affine vertex algebras and minimal affine W-algebras. A level k is called collapsing when the simple minimal affine W-algebra at level k associated with simple Lie superalgebra is isomorphic to its affine vertex subalgebra. We present a proof of complete reducibility of affine vertex algebras at these levels which uses the representation theory of affine algebras and concepts in conformal embeddings (joint project with V. Kac, P. Moseneder-Frajria, P. Papi and O. Perse). The existence of indecomposable and logarithmic modules will be discussed. We also present some results for affine fusion rules at collapsing levels.

Vertex algebra ; W-algebra ; collapsing levels

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