Manuscripta Mathematica

, Volume 136, Issue 1–2, pp 185–197 | Cite as

A general form of Gelfand–Kazhdan criterion

  • Binyong Sun
  • Chen-Bo ZhuEmail author


We formalize the notion of matrix coefficients for distributional vectors in a representation of a real reductive group, which consist of generalized functions on the group. As an application, we state and prove a Gelfand–Kazhdan criterion for a real reductive group in very general settings.

Mathematics Subject Classification (2000)

22E46 (Primary) 


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Copyright information

© Springer-Verlag 2011

Authors and Affiliations

  1. 1.Academy of Mathematics and Systems ScienceChinese Academy of SciencesBeijingPeople’s Republic of China
  2. 2.Department of MathematicsNational University of SingaporeSingaporeSingapore

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