Advertisement

Weighted Orbital Integrals

  • Rebecca A. Herb
Part of the Progress in Mathematics book series (PM, volume 40)

Abstract

Let G be a reductive Lie group of Harish-Chandra class, K a maximal compact subgroup of G, and θ the corresponding Cartan involution. Suppose initially that rank G = rank K so that G has discrete series representations. Then Harish-Chandra has proved the following theorem relating orbital integrals of matrix coefficients and characters for discrete series representations.

Keywords

Wave Packet Conjugacy Class Parabolic Subgroup Cusp Form Discrete Series 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1](a)
    J. Arthur, (a) The characters of discrete series as orbital integrals, Inv. Math. 32 (1976), 205–261.CrossRefGoogle Scholar
  2. (b).
    On the invariant distributions associated to weighted orbital integrals, preprint.Google Scholar
  3. [2](a)
    Harish-Chandra, (a) Discrete series for semisimple Lie groups II, Acta Math. 116 (1966), 1–111.CrossRefGoogle Scholar
  4. (b).
    Harmonic analysis on real reductive groups, I, J. Funct. Anal. 19 (1975), 104–204.CrossRefGoogle Scholar
  5. (c).
    Harmonic analysis on real reductive groups III, Ann. of Math 104 (1976), 117–201.CrossRefGoogle Scholar
  6. [3](a)
    R. Herb, (a) Discrete series characters and Fourier inversion on semisimple real Lie groups, to appear Trans. AMS.Google Scholar
  7. (b).
    Characters of induced representations and weighted orbital integrals, to appear Pacific J. Math.Google Scholar
  8. (c).
    An inversion formula for weighted orbital integrals, to appear Compositio Math.Google Scholar

Copyright information

© Birkhäuser Boston, Inc. 1983

Authors and Affiliations

  • Rebecca A. Herb

There are no affiliations available

Personalised recommendations