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Lie Groups pp 337-347 | Cite as

Mackey Theory

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

Abstract

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.

Keywords

Abelian Group Finite Group Class Function Borel Subgroup Principal 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.

References

  1. 26.
    F. Bruhat. Sur les représentations induites des groupes de Lie. Bull. Soc. Math. France, 84:97–205, 1956.MathSciNetMATHGoogle 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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