Some results about geometric Whittaker model

Roman Bezrukavnikov, Alexander Braverman, Ivan Mirkovic

Research output: Contribution to journalArticlepeer-review

14 Citations (Scopus)


Let G be an algebraic reductive group over a field of positive characteristic. Choose a parabolic subgroup P in G and denote by U its unipotent radical. Let X be a G-variety. The purpose of this paper is to give two examples of a situation in which the functor of averaging of ℓ-adic sheaves on X with respect to a generic character χ:U→Ga commutes with Verdier duality. Namely, in the first example we take X to be an arbitrary G-variety and we prove the above property for all U-equivariant sheaves on X where U is the unipotent radical of an opposite parabolic subgroup; in the second example we take X=G and we prove the corresponding result for sheaves which are equivariant under the adjoint action (the latter result was conjectured by B. C. Ngo who proved it for G=GL(n)). As an application of the proof of the first statement we reprove a theorem of N. Katz and G. Laumon about local acyclicity of the kernel of the Fourier-Deligne transform.

Original languageEnglish
Pages (from-to)143-152
Number of pages10
JournalAdvances in Mathematics
Issue number1
Publication statusPublished - 1 Aug 2004
Externally publishedYes


  • Fourier-Deligne transform
  • Reductive groups
  • Whittaker model


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