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arXiv · 1603.00327

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

Jens Niklas Eberhardt
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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.

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BibTeXRIS

Jens Niklas Eberhardt. 2016-03-01. Graded and Geometric Parabolic Induction for Category $\mathcal{O}$. https://arxiv.org/abs/1603.00327

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