Coherent Springer theory and categorical Deligne-Langlands

Geometry, Symmetry and Physics
Event time: 
Monday, November 2, 2020 - 4:30pm
Location: (password was emailed by Ivan on 9/11, also available from Ivan by email)
Harrison Chen
Speaker affiliation: 
Event description: 

Kazhdan and Lusztig proved the Deligne-Langlands conjecture, a bijection between irreducible representations of principal block representations of a p-adic group with certain unipotent Langlands parameters (a q-commuting semisimple-nilpotent pair) in the Langlands dual group.  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 of coherent sheaves equivalent to modules for the affine Hecke algebra (or specializing at q, smooth 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.