What's special about special? - David Vogan (MIT)

Both conjugacy classes of nilpotent matrices (of size n) and irreducible representations of the symmetric group Sn are indexed by partitions of n. For any complex reductive group, there is a (finite) collection of conjugacy classes of nilpotent Lie algebra elements, and a (finite) set of irreducible Weyl group representations, both enumerated by the 1950s. One might therefore hope for a relationship between these finite sets. I'll first explain Springer's (somewhat complicated) description of such a relationship, and then Lusztig's identification of a bijection between what he called special Weyl group representations and special nilpotent orbits.

I'll explain how these ideas arise in the representation theory of real reductive groups, and what light that might shed on Lusztig's definition of special.

Видео What's special about special? - David Vogan (MIT) канала University of Chicago Department of Mathematics