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The local and global versions of the Whittaker category
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Given a category C acted on by the loop group G((t)), we define its Whittaker model Whit(C) as C^{N((t)),\chi}, where \chi is a non-degenerate character. We study the properties of this construction. When C is the category of sheaves on the quotient of G((t)) by a congruence subgroup, we find a "finite-dimensional" model for Whit(C); the corresponding geometric object is Drinfeld's compactification, denoted \overline{Bun}_N (with poles and level structure).
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A toy model for the Drinfeld-Lafforgue shtuka construction
In a Betti/topological setting, applying categorical and 2-categorical traces to a Hecke action yields universal shtukas, excursion operators, and an S=T identity.
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