Featured Speaker : Harrison Chen (Cornell)

Title: Coherent Springer theory and categorical Deligne-Langlands

Abstract:

Kazhdan and Lusztig proved the Deligne-Langlands conjecture, a bijection between irreducible representations of unipotent principal block representations of a p-adic group with certain unipotent Langlands parameters in the Langlands dual group (plus the data of certain representations).  We lift this bijection to a statement on the level of categories.  Namely, we define a stack of unipotent Langlands parameters and a coherent sheaf on it, which we call the coherent Springer sheaf, which generates a subcategory of the derived category equivalent to modules for the affine Hecke algebra (or specializing at q, unipotent principal block representations of a p-adic group).  Our approach involves categorical traces, Hochschild homology, and Bezrukavnikov's Langlands dual realizations of the affine Hecke category.  This is a joint work with David Ben-Zvi, David Helm and David Nadler.

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