Some analogs of Hilb^n(S) for reductive groups

13.06.2023 13:15 - 14:45

Oscar Kivinen (EPFL)

I will introduce several versions of a class of varieties attached to a reductive group G. These varieties have a representation-theoretic definition and are usually mildly singular. When G=GL_n the different versions are all smooth and coincide with Hilbert schemes of n points on various rational surfaces. 

 

In general, the situation is more subtle and even in the type A case the interplay between the different versions is related to questions about the geometry of the isospectral Hilbert scheme. These varieties are closely related to the representation theory of Cherednik algebras, and coherent sheaves on them are expected to carry information about for example harmonic analysis on the Langlands dual (loop) group as well as Hochschild homology of Rouquier complexes for the corresponding braid group.

Organiser:

H. Grobner, A. Mellit

Location:

SR 12, 2. OG, OMP 1