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

Qijun Tan; Yijun Yao; Shilin Yu

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arXiv · 1610.04103

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

Qijun Tan·Yijun Yao·Shilin Yu

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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 $SL(2,\mathbb{R})$ by considering families of $\D$-modules over its flag varieties. We make a conjecture which gives a geometric understanding of the Makcey-Higson bijection in the general case.

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BibTeX RIS

Qijun Tan, Yijun Yao, Shilin Yu. 2016-10-13. Mackey analogy via $\mathcal{D}$-modules in the example of $SL(2,\mathbb{R})$. https://arxiv.org/abs/1610.04103

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