Mackey analogy as deformation of D -modules

Shilin Yu

doi:10.1007/s00208-021-02332-1

Mackey analogy as deformation of D -modules

Shilin Yu^*

^*Corresponding author for this work

Xiamen University

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

1 Scopus citations

Abstract

Given a real reductive linear Lie group G_R, the Mackey analogy is a bijection between the set of irreducible tempered representations of G_R and the set of irreducible unitary representations of its Cartan motion group, established by Higson and Afgoustidis. We show that this bijection arises naturally from families of twisted D-modules over the ag variety of G_R.

Original language	English
Pages (from-to)	421-457
Number of pages	37
Journal	Mathematische Annalen
Volume	385
Issue number	1-2
DOIs	https://doi.org/10.1007/s00208-021-02332-1
State	Published - Feb 2023
Externally published	Yes

Keywords

Connes-Kasparov isomorphism
D-modules
Harish-Chandra modules
Mackey-Higson-Afgoustidis bijection
Tempered representations

Access to Document

10.1007/s00208-021-02332-1

Cite this

@article{588782953de945bd90ef79768976379d,

title = "Mackey analogy as deformation of D -modules",

abstract = "Given a real reductive linear Lie group GR, the Mackey analogy is a bijection between the set of irreducible tempered representations of GR and the set of irreducible unitary representations of its Cartan motion group, established by Higson and Afgoustidis. We show that this bijection arises naturally from families of twisted D-modules over the ag variety of GR.",

keywords = "Connes-Kasparov isomorphism, D-modules, Harish-Chandra modules, Mackey-Higson-Afgoustidis bijection, Tempered representations",

author = "Shilin Yu",

note = "Publisher Copyright: {\textcopyright} 2022, The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature.",

year = "2023",

month = feb,

doi = "10.1007/s00208-021-02332-1",

language = "英语",

volume = "385",

pages = "421--457",

journal = "Mathematische Annalen",

issn = "0025-5831",

publisher = "Springer New York",

number = "1-2",

}

TY - JOUR

T1 - Mackey analogy as deformation of D -modules

AU - Yu, Shilin

PY - 2023/2

Y1 - 2023/2

N2 - Given a real reductive linear Lie group GR, the Mackey analogy is a bijection between the set of irreducible tempered representations of GR and the set of irreducible unitary representations of its Cartan motion group, established by Higson and Afgoustidis. We show that this bijection arises naturally from families of twisted D-modules over the ag variety of GR.

AB - Given a real reductive linear Lie group GR, the Mackey analogy is a bijection between the set of irreducible tempered representations of GR and the set of irreducible unitary representations of its Cartan motion group, established by Higson and Afgoustidis. We show that this bijection arises naturally from families of twisted D-modules over the ag variety of GR.

KW - Connes-Kasparov isomorphism

KW - D-modules

KW - Harish-Chandra modules

KW - Mackey-Higson-Afgoustidis bijection

KW - Tempered representations

UR - https://www.scopus.com/pages/publications/85122658226

U2 - 10.1007/s00208-021-02332-1

DO - 10.1007/s00208-021-02332-1

M3 - 文章

AN - SCOPUS:85122658226

SN - 0025-5831

VL - 385

SP - 421

EP - 457

JO - Mathematische Annalen

JF - Mathematische Annalen

IS - 1-2

ER -

Mackey analogy as deformation of D -modules

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Cite this