Strong contraction, the mirabolic group and the Kirillov conjecture

E. M. Subag; E. M. Baruch

doi:10.1088/1742-6596/1194/1/012104

Strong contraction, the mirabolic group and the Kirillov conjecture

E. M. Subag, E. M. Baruch

Mathematics

Research output: Contribution to journal › Conference article › peer-review

Abstract

We lift any (infinitesimal) unitary irreducible representation of GL_n(ℝ) to a family of representations that strongly contracts to a certain type of (infinitesimal) unitary irreducible representations of ℝⁿ ⋊ M_n , with M_n being the mirabolic subgroup of GL_n(ℝ). For the case of n = 2 we obtain the full unitary dual of ℝ² ⋊ M ₂ as a strong contraction. We demonstrate the role of the Kirillov conjecture and Kirillov model for these contractions.

Original language	English (US)
Article number	012104
Journal	Journal of Physics: Conference Series
Volume	1194
Issue number	1
DOIs	https://doi.org/10.1088/1742-6596/1194/1/012104
State	Published - Apr 24 2019
Event	32nd International Colloquium on Group Theoretical Methods in Physics, ICGTMP 2018 - Prague, Czech Republic Duration: Jul 9 2018 → Jul 13 2018

All Science Journal Classification (ASJC) codes

General Physics and Astronomy

Access to Document

10.1088/1742-6596/1194/1/012104

Cite this

@article{5061b6f71e8c48d297e77811c16fa2ea,

title = "Strong contraction, the mirabolic group and the Kirillov conjecture",

abstract = "We lift any (infinitesimal) unitary irreducible representation of GLn(ℝ) to a family of representations that strongly contracts to a certain type of (infinitesimal) unitary irreducible representations of ℝn ⋊ Mn , with Mn being the mirabolic subgroup of GLn(ℝ). For the case of n = 2 we obtain the full unitary dual of ℝ2 ⋊ M 2 as a strong contraction. We demonstrate the role of the Kirillov conjecture and Kirillov model for these contractions.",

author = "Subag, {E. M.} and Baruch, {E. M.}",

note = "Publisher Copyright: {\textcopyright} 2019 Published under licence by IOP Publishing Ltd.; 32nd International Colloquium on Group Theoretical Methods in Physics, ICGTMP 2018 ; Conference date: 09-07-2018 Through 13-07-2018",

year = "2019",

month = apr,

day = "24",

doi = "10.1088/1742-6596/1194/1/012104",

language = "English (US)",

volume = "1194",

journal = "Journal of Physics: Conference Series",

issn = "1742-6588",

publisher = "IOP Publishing Ltd.",

number = "1",

}

TY - JOUR

T1 - Strong contraction, the mirabolic group and the Kirillov conjecture

AU - Subag, E. M.

AU - Baruch, E. M.

PY - 2019/4/24

Y1 - 2019/4/24

N2 - We lift any (infinitesimal) unitary irreducible representation of GLn(ℝ) to a family of representations that strongly contracts to a certain type of (infinitesimal) unitary irreducible representations of ℝn ⋊ Mn , with Mn being the mirabolic subgroup of GLn(ℝ). For the case of n = 2 we obtain the full unitary dual of ℝ2 ⋊ M 2 as a strong contraction. We demonstrate the role of the Kirillov conjecture and Kirillov model for these contractions.

AB - We lift any (infinitesimal) unitary irreducible representation of GLn(ℝ) to a family of representations that strongly contracts to a certain type of (infinitesimal) unitary irreducible representations of ℝn ⋊ Mn , with Mn being the mirabolic subgroup of GLn(ℝ). For the case of n = 2 we obtain the full unitary dual of ℝ2 ⋊ M 2 as a strong contraction. We demonstrate the role of the Kirillov conjecture and Kirillov model for these contractions.

UR - http://www.scopus.com/inward/record.url?scp=85065587250&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85065587250&partnerID=8YFLogxK

U2 - 10.1088/1742-6596/1194/1/012104

DO - 10.1088/1742-6596/1194/1/012104

M3 - Conference article

AN - SCOPUS:85065587250

SN - 1742-6588

VL - 1194

JO - Journal of Physics: Conference Series

JF - Journal of Physics: Conference Series

IS - 1

M1 - 012104

T2 - 32nd International Colloquium on Group Theoretical Methods in Physics, ICGTMP 2018

Y2 - 9 July 2018 through 13 July 2018

ER -

Strong contraction, the mirabolic group and the Kirillov conjecture

Abstract

All Science Journal Classification (ASJC) codes

Access to Document

Other files and links

Fingerprint

Cite this