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 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.
|Original language||American English|
|Number of pages||19|
|Journal||Publications of the Research Institute for Mathematical Sciences|
|State||Published - 2021|
Bibliographical noteFunding Information:
We would like to thank Alexander Braverman, Victor Ginzburg, Sam Gunningham, George Lusztig and Kostiantyn Tolmachov for helpful discussions.
© 2021 Research Institute for Mathematical Sciences, Kyoto University. All rights reserved.
- Character sheaves
- Perverse sheaves