Application I: Some Conjectures by B. Gross and D. Prasad: Restrictions of Tempered Representations of SO(n + 1,  1) to SO(n,  1)

  • Toshiyuki Kobayashi
  • Birgit Speh
Part of the Lecture Notes in Mathematics book series (LNM, volume 2234)


Inspired by automorphic forms and L-functions, B. Gross and D. Prasad published in 1992 conjectured about the restriction of irreducible tempered representations of special orthogonal groups SO(p + 1, q) to a special orthogonal subgroup SO(p, q).


  1. 1.
    J. Adams, D. Barbasch, D.A. Vogan, Jr., The Langlands Classification and Irreducible Characters for Real Reductive Groups. Progr. Math., vol. 104 (Birkhäuser Boston, Boston, MA, 1992)Google Scholar
  2. 3.
    J. Arthur, Classifying automorphic representations, in Current Developments in Mathematics 2012 (Int. Press, Somerville, MA, 2013), pp. 1–58Google Scholar
  3. 12.
    W.T. Gan, B.H. Gross, D. Prasad, J.-L. Waldspurger, Sur les conjectures de Gross et Prasad. I, in Astérique, vol. 346 (Soc. Math. France, 2012), xi+318 pp.Google Scholar
  4. 14.
    B.H. Gross, D. Prasad, On the decomposition of a representations of SOn when restricted to SOn−1. Can. J. Math. 44, 974–1002 (1992)CrossRefGoogle Scholar
  5. 43.
    T. Kobayashi, B. Speh, Symmetry breaking for orthogonal groups and a conjecture by B. Gross and D. Prasad, in Geometric Aspects of the Trace Formula, Simons Symposia, ed. by W. Müller et al. (Springer, 2018), pp. 245–266. Available also at arXiv:1702.00263. Google Scholar
  6. 49.
    R.P. Langlands, On the Functional Equation Satisfied by Eisenstein Series. Lecture Notes in Math., vol. 544 (Springer, New York, 1976)CrossRefGoogle Scholar
  7. 55.
    B. Sun, C.-B. Zhu, Multiplicity one theorems: the Archimedean case. Ann. Math. (2) 175, 23–44 (2012). MathSciNetCrossRefGoogle Scholar
  8. 60.
    D.A. Vogan, Jr., The local Langlands conjecture, in Representation Theory of Groups and Algebras. Contemp. Math., vol. 145 (Amer. Math. Soc., Providence, RI, 1993), pp. 305–379Google Scholar

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© Springer Nature Singapore Pte Ltd. 2018

Authors and Affiliations

  • Toshiyuki Kobayashi
    • 1
    • 2
  • Birgit Speh
    • 3
  1. 1.Graduate School of Mathematical SciencesThe University of TokyoKomabaJapan
  2. 2.Kavli IPMUKashiwaJapan
  3. 3.Department of MathematicsCornell UniversityIthacaUSA

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