Mackey analogy via D-modules for SL (2, R)

Qijun Tan; Yi Jun Yao; Shilin Yu

doi:10.1142/S0129167X17500550

Mackey analogy via D-modules for SL (2, R)

Qijun Tan
, Yi Jun Yao^*
, Shilin Yu

^*此作品的通讯作者

Pennsylvania State University
Fudan University
Chinese University of Hong Kong

科研成果: 期刊稿件 › 文章 › 同行评审

6 引用（Scopus）

摘要

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, R) by considering families of D-modules over its flag varieties. We make a conjecture which gives a geometric understanding of the Makecy-Higson bijection in the general case.

源语言	英语
文章编号	1750055
期刊	International Journal of Mathematics
卷	28
期	7
DOI	https://doi.org/10.1142/S0129167X17500550
出版状态	已出版 - 1 6月 2017
已对外发布	是

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title = "Mackey analogy via D-modules for SL (2, R)",

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, R) by considering families of D-modules over its flag varieties. We make a conjecture which gives a geometric understanding of the Makecy-Higson bijection in the general case.",

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AU - Tan, Qijun

AU - Yao, Yi Jun

AU - Yu, Shilin

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N2 - 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, R) by considering families of D-modules over its flag varieties. We make a conjecture which gives a geometric understanding of the Makecy-Higson bijection in the general case.

AB - 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, R) by considering families of D-modules over its flag varieties. We make a conjecture which gives a geometric understanding of the Makecy-Higson bijection in the general case.

KW - D-modules

KW - Mackey-Higson analogy

KW - admissible representations of SL (2, R)

UR - https://www.scopus.com/pages/publications/85021801877

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DO - 10.1142/S0129167X17500550

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JO - International Journal of Mathematics

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ER -

Mackey analogy via D-modules for SL (2, R)

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