Mackey analogy as deformation of $\mathcal{D}$-modules

Abstract

Given a real reductive group Lie group $G_{\mathbb{R}}$, the Mackey analogy is a bijection between the set of irreducible tempered representations of $G_{\mathbb{R}}$ and the set of irreducible unitary representations of its Cartan motion group. We show that this bijection arises naturally from families of twisted $\mathcal{D}$-modules over the flag variety of $G_{\mathbb{R}}$.

References in corpus (1)

• Mackey analogy via $\mathcal{D}$-modules in the example of $SL(2,\mathbb{R})$