Mackey analogy via $\mathcal{D}$-modules in the example of $SL(2,\mathbb{R})$
Representation Theory
2016-10-14 v1
Abstract
A conjecture by Mackey and Higson claims that there is close relationship between irreducible representations of a real reductive group and those of its Cartan motion group. The case of irreducible tempered unitary representations has been verified recently by Afgoustidis. We study the admissible representations of by considering families of -modules over its flag varieties. We make a conjecture which gives a geometric understanding of the Makcey-Higson bijection in the general case.
Keywords
Cite
@article{arxiv.1610.04103,
title = {Mackey analogy via $\mathcal{D}$-modules in the example of $SL(2,\mathbb{R})$},
author = {Qijun Tan and Yijun Yao and Shilin Yu},
journal= {arXiv preprint arXiv:1610.04103},
year = {2016}
}