The center of affine vertex superalgebras at the critical level via W-algebras
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：Dražen Adamović（University of Zagreb）
： 2025-04-18 10:30
：Conference Room C503 at Administration Building at Haiyun Campus
Speaker：Dražen Adamović（University of Zagreb）
Time：2025-4-18, 10:30
Location：Conference Room C503 at Administration Building at Haiyun Campus
Abstract:
Affine vertex algebras at the critical level belong to the most important examples of vertex algebras. These vertex algebras play a crucial role in the geometric Langlands program. The basic problem for vertex algebras at the critical level is to describe their centers. In the Lie algebra case, the center was described by B. Feigin and E. Frenkel and it is isomorphic to principal affine W-algebras at the critical level. In the Lie superalgebra case, the structure of the center at the critical level is much more complicated since the center need not be finitely generated and the principal affine W-algebras are not commutative. So the basic question is how to identify principal affine W-algebras at the critical level and describe their centers. In this talk we describe recent progress in describing the center for affine vertex superalgebras associated to $\mathfrak{sl}(m \vert n)$. We discuss a general conjecture about the structure of the center and prove it in a number of cases by identifying the associated affine W-algebras. We present details in the case of Lie superalgebra $sl(2 \vert1)$. In this case, we also show how the inverse quantum hamiltonian reduction can be applied on vertex algebras at the critical level. This talk is based on an ongoing project with Boris Feigin and Shigenori Nakatsuka.
