Parabolic induction and perverse sheaves on h/W

Mikhail Kapranov; Vadim Schechtman

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arXiv · 2006.04285

Parabolic induction and perverse sheaves on h/W

Mikhail Kapranov·Vadim Schechtman

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Abstract

For a complex reductive Lie group G with Lie algebra g, Cartan subalgebra h and Weyl group W, we describe the category of perverse sheaves on h/W smooth w.r.t the natural stratification. The answer is given in terms of mixed Bruhat sheaves, which are certain mixed sheaf-cosheaf data on cells of a natural cell decomposition of h/W. Using the parabolic Bruhat decomposition, we relate mixed Bruhat sheaves with the properties of various procedures of parabolic induction and restriction that connect different Levi subgroups in G.

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Mikhail Kapranov, Vadim Schechtman. 2020-06-07. Parabolic induction and perverse sheaves on h/W. https://arxiv.org/abs/2006.04285

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