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arXiv · 1707.00240

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

Shilin Yu
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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 $G_\mathbb{R}$.

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Shilin Yu. 2017-07-02. Mackey analogy as deformation of $\mathcal{D}$-modules. https://arxiv.org/abs/1707.00240

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