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Unitary Representations of SL2 (ℝ)

  • 2025
  • OriginalPaper
  • Chapter
Published in:
Authors
Manfred Einsiedler
Thomas Ward
Published in
Unitary Representations and Unitary Duals
Publisher
Springer Nature Switzerland

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Abstract

The unitary dual of the special linear group in two dimensions is described in detail, and natural unitary representations are decomposed into irreducible representations. The spectral decomposition for the hyperbolic plane is related to the principal series representations. The complementary series representations are used to give a better understanding of the (lack of) spectral gap, decay rates, and integrability exponents. The connection between spectral theory of compact quotients and dynamics is discussed.

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previous chapter Discrete Series Representations and Temperedness for SL2(ℝ)
Title
Unitary Representations of SL2 (ℝ)
Authors
Manfred Einsiedler
Thomas Ward
Copyright Year
2025
Book
Unitary Representations and Unitary Duals

Print ISBN: 978-3-032-03898-2

Electronic ISBN: 978-3-032-03899-9

Copyright Year: 2025

DOI
https://doi.org/10.1007/978-3-032-03899-9_9

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