Skip to Main content Skip to Navigation
New interface

Twisted Whittaker category on affine flags and category of representations of mixed quantum group

Abstract : Suppose that G is a reductive group. We have the geometric Satake equivalence which identifies Sph (G), the perverse G (O) equivalent D-modules on affine grassmannin as the category of finite dimensional representation of H, the Langlands dual group of G. We note that: Whit(Gr) = Sph(G). Here, Whit (Gr) is the module category D (N (K), \ chi) -equivalent on Gr. Now, the category of representation admits a deformation by the category of representations of quantum group. On the Whittaker side, we can consider the twisted D-modules on affine grassmannin. This is the fundamental local equivalence: Whit_q (Gr) = Rep_q (H) . Recently, D. Gaitsgory proposed its ramified version. We consider the affine flags instead of the affine grassmannians. In this case, we have to replace the category of quantum group representations with another category, the category of mixed quantum group representations. Whit_q (Fl) = Rep_q ^ {mix} (H) . We prove that the category of twisted Whittaker D-modules on the affine flags and the category of representations of the mixed quantum group are equivalent.
Document type :
Complete list of metadata

Cited literature [90 references]  Display  Hide  Download
Contributor : Thèses UL Connect in order to contact the contributor
Submitted on : Friday, October 2, 2020 - 3:59:37 PM
Last modification on : Wednesday, November 3, 2021 - 4:48:22 AM
Long-term archiving on: : Monday, January 4, 2021 - 8:39:34 AM


Files produced by the author(s)


  • HAL Id : tel-02956301, version 1



Ruotao Yang. Twisted Whittaker category on affine flags and category of representations of mixed quantum group. Representation Theory [math.RT]. Université de Lorraine, 2020. English. ⟨NNT : 2020LORR0064⟩. ⟨tel-02956301⟩



Record views


Files downloads