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鉁掞笍 TITRE / TITLE
Perverse sheaves and representations of p-adic groups
馃搫 R脡SUM脡 / ABSTRACT
One of the first basic ideas we all learn is that a continuous function is determined by its values on a dense open subset. In representation theory, this allows us to recognize a representation of a Lie group from an especially well-behaved locus---that of regular semisimple elements. But what if we want to study representations of matrix groups over finite fields? Lusztig's revolutionary idea in the 1980s was to replace the analytic notion of limit in the continuous setting by the algebro-geometric notion of intermediate extension in this discrete setting.
I will explain this picture and describe a recent construction (joint with R. Bezrukavnikov) of perverse sheaves that give rise to positive-depth supercuspidal representations of p-adic groups. In the simplest nontrivial case, this resolves a conjecture of Lusztig.
馃搷 LIEU / PLACE
Hybride - CRM, Salle / Room 5340, Pavillon Andr茅 Aisenstadt
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