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Algebra
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David Helm, PMA 9.166: A categorical Deligne-Langlands correspondence for split reductive groups
Thursday, October 13, 2022, 10:00am - 11:00am
Let G be a split reductive group over a p-adic field F. We construct a natural coherent sheaf on the moduli stack of unipotent Langlands parameters for G, called the coherent Springer sheaf, whose self-Ext algebra is naturally isomorphic to the Iwahori Hecke algebra for G. As a consequence we deduce the existence of a fully faithful embedding of the Iwahori block of the category of smooth representations of G into the derived category of ind-coherent sheaves on the moduli stack of Langlands parameters. For G = GL_n we can go further and construct a fully faithful embedding of the category of all smooth representations of G into this derived category.
Location: PMA 9.166

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