Parabolic induction and the Harish-Chandra D-module

2021/03/25 by Ginzburg, Victor
#Algebraic Geometry (math.AG) #FOS: Mathematics #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.2103.13594

Abstract

Let G be a reductive group and L a Levi subgroup. Parabolic induction and restriction are a pair of adjoint functors between Ad-equivariant derived categories of either constructible sheaves or (not necessarily holonomic) D-modules on G and L, respectively. Bezrukavnikov and Yom Din proved, generalizing a classic result of Lusztig, that these functors are exact. In this paper, we consider a special case where L=T is a maximal torus. We give explicit formulas for parabolic induction and restriction in terms of the Harish-Chandra D-module on G x T. We show that this module is flat over D(T), which easily implies that parabolic induction and restriction are exact functors between the corresponding abelian categories of D-modules.

Related

• On parabolic restriction of perverse sheaves
• Derived parabolic induction
• Universal hierarchical structure of reducibility of Harish-Chandra parabolic induction
• Graded and Geometric Parabolic Induction for Category O
• On the Right Derived Functors of Ordinary Parts