The local and global versions of the Whittaker category

2018/11/06 by Gaitsgory, Dennis · 2 citations
#Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1811.02468

Abstract

Given a category C acted on by the loop group G((t)), we define its Whittaker model Whit(C) as C^N((t)),χ, where χis 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 Bun_N (with poles and level structure).

Cited by

• On a tamely ramified local relative Langlands conjecture via categorical representations
• Local and global Langlands conjecture(s) over function fields

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