Strong contraction, the mirabolic group and the Kirillov conjecture

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 ful...

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Bibliographic Details
Published in:Journal of physics. Conference series 2019-04, Vol.1194 (1), p.12104
Main Authors: Subag, E M, Baruch, E M
Format: Article
Language:English
Subjects:
Representations
Subgroups
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Summary: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 ⋊ M2 as a strong contraction. We demonstrate the role of the Kirillov conjecture and Kirillov model for these contractions.
ISSN:1742-6588
1742-6596
DOI:10.1088/1742-6596/1194/1/012104