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

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

6 Scopus citations

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.

Original language	English
Article number	1750055
Journal	International Journal of Mathematics
Volume	28
Issue number	7
DOIs	https://doi.org/10.1142/S0129167X17500550
State	Published - 1 Jun 2017
Externally published	Yes

Keywords

D-modules
Mackey-Higson analogy
admissible representations of SL (2, R)

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10.1142/S0129167X17500550

Cite this

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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.",

keywords = "D-modules, Mackey-Higson analogy, admissible representations of SL (2, R)",

author = "Qijun Tan and Yao, \{Yi Jun\} and Shilin Yu",

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AU - Tan, Qijun

AU - Yao, Yi Jun

AU - Yu, Shilin

PY - 2017/6/1

Y1 - 2017/6/1

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

U2 - 10.1142/S0129167X17500550

DO - 10.1142/S0129167X17500550

M3 - 文章

AN - SCOPUS:85021801877

SN - 0129-167X

VL - 28

JO - International Journal of Mathematics

JF - International Journal of Mathematics

IS - 7

M1 - 1750055

ER -

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

Abstract

Keywords

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