Mackey analogy as deformation of $\mathcal{D}$-modules
@article{Yu2017MackeyAA,
title={Mackey analogy as deformation of \$\mathcal\{D\}\$-modules},
author={Shilin Yu},
journal={arXiv: Representation Theory},
year={2017}
}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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