Strong contraction, the mirabolic group and the Kirillov conjecture

E. M. Subag, E. M. Baruch

Research output: Contribution to journalConference article

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.

Original languageEnglish (US)
Article number012104
JournalJournal of Physics: Conference Series
Volume1194
Issue number1
DOIs
StatePublished - Apr 24 2019
Event32nd International Colloquium on Group Theoretical Methods in Physics, ICGTMP 2018 - Prague, Czech Republic
Duration: Jul 9 2018Jul 13 2018

Fingerprint

contraction
subgroups

All Science Journal Classification (ASJC) codes

  • Physics and Astronomy(all)

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.}",
year = "2019",
month = "4",
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",

}

Strong contraction, the mirabolic group and the Kirillov conjecture. / Subag, E. M.; Baruch, E. M.

In: Journal of Physics: Conference Series, Vol. 1194, No. 1, 012104, 24.04.2019.

Research output: Contribution to journalConference article

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

VL - 1194

JO - Journal of Physics: Conference Series

JF - Journal of Physics: Conference Series

SN - 1742-6588

IS - 1

M1 - 012104

ER -