Lie Groups pp 337-347 | Cite as

Mackey Theory

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


Given a subgroup H of a finite group G, and a representation π of H, there is an induced representation π G of G. Mackey theory is concerned with intertwining operators between a pair of induced representations. It is based on a very simple idea: if the two representations are induced from subgroups H 1 and H 2, then every such intertwining operator is convolution with suitable function Δ, which has left and right translation properties by H 1 and H 2. This leads to a method of calculating the space of intertwining operators, based on the double cosets H 2\G/H 1.


Abelian Group Finite Group Class Function Borel Subgroup Principal Series 
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  1. 26.
    F. Bruhat. Sur les représentations induites des groupes de Lie. Bull. Soc. Math. France, 84:97–205, 1956.MathSciNetzbMATHGoogle 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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