Geometric construction of semicanonical bases and crystals of (affine) Lie algebras via quivers and Higgs bundles

Speaker:

Guillaume Pouchin

Affiliation:

U Paris 6/MPI

Date:

Thu, 2011-05-12 15:00 - 16:00

Location:

MPIM Lecture Hall [2]

Parent event:

MPI-Oberseminar [3]

In this talk I will present the construction of enveloping Lie algebras via constructible fonctions on a stack of representation of a quiver (by Lusztig), as well as the geometric construction of the crystal (by Kashiwara-Saito).
I will then present how this techniques can be translated in the framework of Higgs bundles on a curve, in order to obtain loop Lie algebras.