  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.
