On Parabolic Restriction of Perverse Sheaves

  • Roman Bezrukavnikov

    Massachusetts Institute of Technology, Cambridge, USA
  • Alexander Yom Din

    The Hebrew University of Jerusalem, Israel
On Parabolic Restriction of Perverse Sheaves cover
Download PDF

A subscription is required to access this article.

Abstract

We prove exactness of parabolic restriction and induction functors for conjugation equivariant sheaves on a reductive group generalizing a well-known result of Lusztig who established this property for character sheaves. We propose a conjectural (but known for character sheaves) tt-exactness property of the Harish-Chandra transform and provide evidence for that conjecture. We also present two applications generalizing some results of Gabber and Loeser on perverse sheaves on an algebraic torus to an arbitrary reductive group.

Cite this article

Roman Bezrukavnikov, Alexander Yom Din, On Parabolic Restriction of Perverse Sheaves. Publ. Res. Inst. Math. Sci. 57 (2021), no. 3/4, pp. 1089–1107

DOI 10.4171/PRIMS/57-3-12