What’s special about special?

Date/heure
5 décembre 2024
16:30 - 17:30

Lieu
Amphithéâtre Hedy Lamarr – UFR MIM – Metz

Oratrice ou orateur
David Vogan (M.I.T.)

Catégorie d'évènement
Colloquium

Both conjugacy classes of nilpotent matrices (of size $n$) and
irreducible representations of the symmetric group $S_n$ 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 {\em bijection} between what he
called {\em special} Weyl group representations and {\em 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.