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

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10.1088/1742-6596/1194/1/012104

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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.",

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AU - Subag, E. M.

AU - Baruch, E. M.

PY - 2019/4/24

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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.

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UR - https://www.scopus.com/pages/publications/85065587250#tab=citedBy

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

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