# 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…

## 8 Citations

### On the Deligne–Lusztig involution for character sheaves

- MathematicsSelecta Mathematica
- 2019

For a reductive group G, we study the Drinfeld-Gaitsgory functor of the category of conjugation-equivariant D-modules on G. We show that this functor is an equivalence of categories, and that it has…

### Exterior powers of a parabolic Springer sheaf

- Mathematics
- 2022

We compute the exterior powers, with respect to the perversely truncated multiplicative convolution, of a parabolic Springer sheaf corresponding to a maximal parabolic subgroup ﬁxing a line in the…

### Notes on a conjecture of Braverman-Kazhdan

- Mathematics
- 2019

Given a connected reductive algebraic group G over a finite field together with a representation of the dual group of G in GL(n), Braverman and Kazhdan defined an exotic Fourier operator on the space…

### A vanishing conjecture: the GL_n case

- Mathematics
- 2019

In this article we propose a vanishing conjecture for a certain class of $\ell$-adic complexes on a reductive group G, which can be regraded as a generalization of the acyclicity of the…

### Monodromic model for Khovanov–Rozansky homology

- MathematicsJournal für die reine und angewandte Mathematik (Crelles Journal)
- 2022

Abstract We describe a new geometric model for the Hochschild cohomology of Soergel bimodules based on the monodromic Hecke category studied earlier by the first author and Yun. Moreover, we identify…

### Deligne-Lusztig duality on the moduli stack of bundles

- Mathematics
- 2020

Let $Bun_G(X)$ be the moduli stack of $G$-torsors on a smooth projective curve $X$ for a reductive group $G$. We prove a conjecture made by Drinfeld-Wang and Gaitsgory on the Deligne-Lusztig duality…

### Correction to: Generalized Springer theory for D-modules on a reductive Lie algebra

- MathematicsSelecta Mathematica
- 2021

In this note, we note the errata in Gunningham (2018) and give revised proofs of the main results (which remain true as stated). The author would like to thank Victor Ginzburg for bringing these…

### A generalization of the b-function lemma

- MathematicsCompositio Mathematica
- 2021

We establish some cohomological bounds in $D$-module theory that are known in the holonomic case and folklore in general. The method rests on a generalization of the $b$-function lemma for…

## References

SHOWING 1-10 OF 22 REFERENCES

### The characteristic cycle and the singular support of a constructible sheaf

- Mathematics
- 2015

We define the characteristic cycle of an étale sheaf as a cycle on the cotangent bundle of a smooth variety in positive characteristic using the singular support recently defined by Beilinson. We…

### Hyperbolic localization of intersection cohomology

- Mathematics
- 2002

AbstractFor a normal variety X defined over an
algebraically closed field with an action of the multiplicative group T = Gm, we consider the "hyperbolic localization" functor Db(X) → Db(XT), which…

### The Gauss map and a noncompact Riemann-Roch formula for constructible sheaves on semiabelian varieties

- Mathematics
- 1999

For an irreducible subvariety Z in an algebraic group G we define a nonnegative integer gdeg(Z) as the degree, in a certain sense, of the Gauss map of Z. It can be regarded as a substitution for the…

### A Gauss-Bonnet theorem for constructible sheaves on reductive groups

- Mathematics
- 2002

In this paper, we prove an analog of the Gauss-Bonnet formula for constructible sheaves on reductive groups. This formula holds for all constructible sheaves equivariant under the adjoint action and…

### On Some Finiteness Questions for Algebraic Stacks

- Mathematics
- 2011

We prove that under a certain mild hypothesis, the DG category of D-modules on a quasi-compact algebraic stack is compactly generated. We also show that under the same hypothesis, the functor of…

### ON A THEOREM OF BRADEN

- Mathematics
- 2013

We give a new proof of Braden’s theorem ([Br]) about hyperbolic restrictions of constructible sheaves/D-modules. The main geometric ingredient in the proof is a 1-parameter family that degenerates a…

### A formula for the geometric Jacquet functor and its character sheaf analogue

- Mathematics
- 2015

Let (G,K) be a symmetric pair over the complex numbers, and let $${X=K \backslash G}$$X=K\G be the corresponding symmetric space. In this paper we study a nearby cycles functor associated to a…