The motivic Satake equivalence

Abstract

We refine the geometric Satake equivalence due to Ginzburg, Beilinson-Drinfeld, and Mirković-Vilonen to an equivalence between mixed Tate motives on the double quotient $L^{+}G\backslash LG/L^{+}G$ and representations of Deligne's modification of the Langlands dual group $\hat{G}$.

final published version (v2 contains a new section on sheaves vs. functions, v3 has an overhauled appendix and many more minor edits)

References in corpus (3)

• Perfection in motivic homotopy theory
• The intersection motive of the moduli stack of shtukas
• Tate motives on Witt vector affine flag varieties

Cited by in corpus (4)

• Bessel $F$-isocrystals for reductive groups
• Tate motives on Witt vector affine flag varieties
• The geometric Satake equivalence for integral motives
• Geometrization of the Satake transform for mod $p$ Hecke algebras