Algebra Seminar

Introduced by Lusztig in the eighties, character sheaves are the geometrical counterpart of irreducible representations of finite groups of Lie type. Defined over algebraic groups, they allow us to use geometrical tools to deduce information on the finite groups. In this talk, Marie Roth will give a definition of character sheaves before explaining how to compute their restriction to conjugacy classes (to some extent). This work was part of her PhD thesis under the supervision of Olivier Dudas and Gunter Malle.

Adam Jones will explore the relationship between the category of smooth representations of a semisimple p-adic Lie group G and the module category over its associated pro-p Iwahori-Hecke algebra via the canonical invariance adjunction. This relationship is well understood in characteristic 0, in fact it yields a category equivalence equivalence, but in characteristic p it is very mysterious and largely defies understanding. We will explore methods of constructing an appropriate subcategory of Hecke modules which is well behaved under the adjunction, and which can be shown to contain all parabolic inductions. He will give examples of this yielding results when G has rank 1, and more recently when G = SL_3 in certain cases.

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