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

Pennsylvania State University
Technion-Israel Institute of Technology

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
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 - 24 Apr 2019
Externally published	Yes
Event	32nd International Colloquium on Group Theoretical Methods in Physics, ICGTMP 2018 - Prague, Czech Republic Duration: 9 Jul 2018 → 13 Jul 2018

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© 2019 Published under licence by IOP Publishing Ltd.

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10.1088/1742-6596/1194/1/012104

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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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Strong contraction, the mirabolic group and the Kirillov conjecture

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