On parabolic restriction of perverse sheaves

Research paper by Roman Bezrukavnikov, Alexander Yom Din

Indexed on: 08 Oct '18Published on: 08 Oct '18Published in: arXiv - Mathematics - Representation Theory


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) t-exactness property of the Harish-Chandra transform and provide an 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.