Lie Groups pp 461-469 | Cite as

Gelfand Pairs

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


We recall that a representation θ of a compact group G is called multiplicity-free if in its decomposition into irreducibles,
$$\displaystyle{ \theta =\bigoplus _{i}d_{i}\pi _{i}, }$$
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.


Irreducible Representation Compact Group Endomorphism Ring Double Coset Trivial Representation 
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  1. 59.
    B. Gross. Some applications of Gelfand pairs to number theory. Bull. Amer. Math. Soc. (N.S.), 24:277–301, 1991.Google Scholar

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© Springer Science+Business Media New York 2013

Authors and Affiliations

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

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