Speaker
Emmanuel Letellier
(Université Paris Cité)
Description
Given a finite group $G$, one can define two natural rings: the character ring of $G$ and the center of the group algebra of $G$. When $G$ is abelian, the two rings are isomorphic via a Fourier transform. In the non-abelian case such a Fourier transform does not exist. In this lecture I will discuss the case where $G$ is the general general linear group over a finite field. We will see how to make a bridge between these two rings through the geometry of character varieties (moduli space of local systems on punctured Riemann sphere), the moduli space of Higgs bundles or quiver varieties.
Primary author
Emmanuel Letellier
(Université Paris Cité)
