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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

Unipotent representations and mixed Hodge modules




Date(s) : 12/03/2024   iCal
14h00 - 15h00

Let Pi(G) denote the set of irreducible unitary representations of a semisimple Lie group G. A fundamental problem in representation theory is to describe the structure of this set. In previous joint work with Losev and Matvieievskyi, we have defined a class of representations called rigid unipotent representations, which are conjectured to form the building blocks of Pi(G). Unfortunately, it is not at all clear from their construction that these representations are unitary. In 2011, Schmid and Vilonen proposed a geometric framework for studying unitary representations using Saito’s theory of mixed Hodge modules. In this talk, I will explain how this framework can be applied to prove the unitarity of all rigid unipotent representations. This is based on joint work in progress with Dougal Davis.

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

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