A W-superalgebra is a vertex superalgebra associated to a Lie superalgebra, g, an invariant bilinear form on g and an even nilpotent element in g. If g is a Lie algebra and f is principal nilpotent then one obtains the principal W-algebra of g. Feigin-Frenkel duality are isomorphisms between principal W-algebras. These isomorphisms somehow generalize to non principal nilpotent elements, however the isomorphism is only between coset subalgebras of W-algebras and W-superalgebras. In my talk I will first introduce the isomorphisms that generalize Feigin-Frenkel duality. I then want to outline a program on how to use the dualities to get correspondences between tensor categories of W-algebra modules and dual W-superalgebra modules.

This will be a zoom seminar.

Zoom URL: https://kyoto-u-edu.zoom.us/j/81243802998

passcode: The order of the Weyl group of type $E_6$