报告题目：On the Representation Theory of Affine Vertex Algebras at Conformal and Collapsing Levels

报告人： Drazen Adamovic，University of Zagreb

报告时间：7月24日（周五），上午10点半

地点：新楼312

摘要：

In this talk, we discuss several applications of the theory of conformal embeddings and collapsing levels for affine vertex algebras, initiated in joint papers with Kac, Moseneder Frajria, Papi, and Perše.

We first recall a classification of conformal embeddings of affine vertex algebras into minimal affine W-algebras. Next, we present a proof of the semisimplicity of the Kazhdan–Lusztig category KL_k for affine vertex superalgebras at collapsing and certain other levels.The proof uses the representation theory of affine vertex algebras together with concepts from the theory of conformal embeddings.

Finally, we discuss the decomposition problem for conformal embeddings in several interesting cases.