To each non-zero nilpotent orbit of a simple finite-dimensional Lie superalgebra π€ with a non-degenerate invariant bilinear form one associates a simple vertex algebra, called a quantum affine W-algebra. In the simplest case π€=π°π©2 one gets the Virasoro vertex algebra.
For the smallest simple Lie superalgebras π€ one gets by this construction all N = 1,2,3,4, and big N = 4 superconformal algebras. I will explain classification of unitary representations of W-algebras, associated to nilpotent orbits of minimal dimension in the even part of π€, which cover all the above examples.
This is a joint work with P. Moseneder Frajria and P. Papi.
This video was produced by the International Centre for Mathematical Sciences, as part of the workshop Geometric Representation Theory and W-algebras.
