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Aix-Marseille Université
Institut de Mathématiques de Marseille (I2M) - UMR 7373
Site Saint-Charles : 3 place Victor Hugo, Case 19, 13331 Marseille Cedex 3
Site Luminy : Campus de Luminy - Case 907 - 13288 Marseille Cedex 9

Séminaire

On a geometric parametrization of smooth irreducible p-adic representations




Date(s) : 26/03/2024   iCal
14h00 - 15h00

 Let Irr(G) denote the set of smooth irreducible complex representations of a reductive p-adic group G. The Bernstein decomposition theorem provides us with a natural partition of Pi(G) into Bernstein components, and the irreducible representations on each component are in bijection with those of a Hecke algebra.
In this talk, I will explain how to construct the Lafforgue variety Laf(G), an infinite disjoint union of affine schemes equipped with an open dense subscheme whose geometric points parametrize Pi(G). I will also show it comes equipped with a finite morphism to the Bernstein variety.
Time allowing, I will also report on related work in progress studying how the Lafforgue variety deforms when changing the parameter of an affine Hecke algebra. This is related to a conjecture by Aubert, Baum and Plymen.

Emplacement
I2M Luminy - TPR2, Salle de Séminaire 304-306 (3ème étage)

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