On Parabolic Restriction of Perverse Sheaves

@article{Bezrukavnikov2021OnPR,
  title={On Parabolic Restriction of Perverse Sheaves},
  author={Roman Bezrukavnikov and Alexander Yom Din},
  journal={Publications of the Research Institute for Mathematical Sciences},
  year={2021}
}
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… 

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