Appendix III: A Translation Functor for G = O(n + 1, 1)

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


In this chapter, we discuss a translation functor for the group G = O(n + 1, 1), which is not in the Harish-Chandra class if n is even, in the sense that \(\operatorname {Ad}(G)\) is not contained in the group \(\operatorname {Int}({\mathfrak {g}}_{\mathbb {C}})\) of inner automorphisms.


  1. 20.
    J.C. Jantzen, Moduln mit einem höchsten Gewicht, in Lecture Notes in Math., vol. 750 (Springer, Berlin/Heidelberg/New York, 1979)Google Scholar
  2. 53.
    B. Speh, D.A. Vogan, Jr., Reducibility of generalized principal series representations. Acta Math. 145, 227–299 (1980)MathSciNetCrossRefGoogle Scholar
  3. 59.
    D.A. Vogan, Jr., Representations of Real Reductive Lie Groups. Progr. Math., vol. 15 (Birkhäuser, Boston, MA, 1981), xvii+754 pp.Google Scholar
  4. 65.
    G. Zuckerman, Tensor products of finite and infinite dimensional representations of semisimple Lie groups. Ann. Math. (2) 106, 295–308 (1977)MathSciNetCrossRefGoogle Scholar

Copyright information

© 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

Personalised recommendations