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arXiv · 1811.11132

Strong contraction, the mirabolic group and the Kirillov conjecture

Eyal M. Subag·Ehud Moshe Baruch
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Abstract

We lift any (infinitesimal) unitary irreducible representation of $GL_n(\mathbb{R})$ to a family of representations that strongly contracts to a certain type of (infinitesimal) unitary irreducible representations of $\mathbb{R}^n\rtimes {M}_n$, with $M_n$ being the mirabolic subgroup of $GL_n(\mathbb{R})$. For the case of $n=2$ we obtain the full unitary dual of $\mathbb{R}^2\rtimes {M}_2$ as a strong contraction. We demonstrate the role of the Kirillov conjecture and Kirillov model for these contractions.

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Eyal M. Subag, Ehud Moshe Baruch. 2018-11-27. Strong contraction, the mirabolic group and the Kirillov conjecture. https://doi.org/10.1088/1742-6596%2F1194%2F1%2F012104

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