The Mackey-Higson bijection and twisted characteristic variety:

Connes and Higson pointed out that the Baum-Connes conjecture in operator algebra suggests a surprising analogy between the tempered dual of a real reductive group and that of its Cartan motion group, which was first observed by Mackey in 1970's. Recently the Mackey-Higson bijection has been established by Afgoustidis. However, the reason for the existence of this bijection is not immediately clear. In this talk, I will show that this bijection follows naturally from deformation of Harish-Chandra D-modules. The construction leads to a new notion of `twisted' characteristic varieties of D-modules, which are Lagrangian subvarieties of the twisted cotangent bundle of the flag variety.