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Lie Groups pp 461-469 | Cite as

Gelfand Pairs

  • Daniel Bump
Chapter
Part of the Graduate Texts in Mathematics book series (GTM, volume 225)

Abstract

We recall that a representation θ of a compact group G is called multiplicity-free if in its decomposition into irreducibles,
$$\displaystyle{ \theta =\bigoplus _{i}d_{i}\pi _{i}, }$$
(45.1)
each irreducible representation π i occurs with multiplicity d i = 0 or 1. A common situation that we have seen already several times is for a group GH to have the property that for some representation τ of H the induced representation \(\mathrm{Ind}_{H}^{G}(\tau)\) is multiplicity-free.

Keywords

Irreducible Representation Compact Group Endomorphism Ring Double Coset Trivial Representation 
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.

References

  1. 59.
    B. Gross. Some applications of Gelfand pairs to number theory. Bull. Amer. Math. Soc. (N.S.), 24:277–301, 1991.Google Scholar

Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  • Daniel Bump
    • 1
  1. 1.Department of MathematicsStanford UniversityStanfordUSA

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