Graded and Geometric Parabolic Induction for Category $\mathcal{O}$

Abstract

We prove that the parabolic induction functor on BGG-category $\mathcal{O}$ associated to a complex reductive Lie algebra is gradable, that is, lifts to graded category $\mathcal{O}$ as constructed by Beilinson-Ginzburg-Soergel. Graded category $\mathcal{O}$ is equivalent to a category of stratified mixed Tate motives on a corresponding flag variety as recently defined by Soergel-Wendt. The graded version of parabolic induction is induced by a geometric parabolic induction functor we construct on the level of stratified mixed Tate motives. We also describe the effect of parabolic induction on the level of Soergel modules.

Completely reworked, added the case of singular weights

References in corpus (1)

• Triangulated categories of mixed motives

Cited by in corpus (1)

• K-Motives and Koszul Duality