25 jan 2023 -- 11:30
Aula Tricerri, DIMaI, Firenze
Seminario di Geometria del Dini
Abstract.
We will construct the Lafforgue variety, a parametrizing space for the smooth irreducible representations of a p-adic reductive group G(F). Our main tools will be Hecke algebras and a noncommutative version of the Hilbert scheme. The Lafforgue variety comes equipped with a finite projection to the Bernstein variety, which is a bijection outside the locus of a regular function that we call discriminant, generalizing the classical discriminant of algebraic number theory to a non-commutative setting. As an application, we study irreducibility of induced representations and recover classical results in the case of principal series.