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October 2021 A contraction of the principal series representations of $SL(2,\mathbf{R})$
Benjamin Cahen
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Kodai Math. J. 44(3): 422-436 (October 2021). DOI: 10.2996/kmj/kmj44302

Abstract

We introduce and study a contraction of the principal series representations of $SL(2,\mathbf{R})$ to the unitary irreducible representations of the Heisenberg group. We interpret the contraction results in terms of Weyl correspondences on the coadjoint orbits associated with the representations.

Acknowledgment

I would like to thank the Referee for a careful reading of the manuscript and for some relevant remarks.

Citation

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Benjamin Cahen. "A contraction of the principal series representations of $SL(2,\mathbf{R})$." Kodai Math. J. 44 (3) 422 - 436, October 2021. https://doi.org/10.2996/kmj/kmj44302

Information

Received: 23 November 2020; Revised: 5 March 2021; Published: October 2021
First available in Project Euclid: 27 October 2021

Digital Object Identifier: 10.2996/kmj/kmj44302

Subjects:
Primary: 22E46
Secondary: 22E45 , 81R05 , 81S10

Keywords: $SL(2,\mathbf{R})$ , coadjoint orbits , contractions of Lie groups , contractions of representations , Heisenberg group , Weyl correspondence

Rights: Copyright © 2021 Tokyo Institute of Technology, Department of Mathematics

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Vol.44 • No. 3 • October 2021
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