Free Extensions of Group Actions, Induced Representations, and the Foundations of Physics

  • David J. Foulis
  • Alexander Wilce
Part of the Fundamental Theories of Physics book series (FTPH, volume 111)


Given a group G and a subgroup H of G, any action of H on a set S admits a canonical free extension to an action of the larger group G on a larger set X = G × H S. In this expository article (supplementary to the individual contributions of the authors), we outline the theory of such free extensions, and the parallel notion of the unitary representation of G induced by a unitary representation of H. To keep matters simple, we restrict our attention almost wholly to actions of finite groups on finite sets and finite-dimensional unitary spaces.


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Copyright information

© Springer Science+Business Media Dordrecht 2000

Authors and Affiliations

  • David J. Foulis
    • 1
  • Alexander Wilce
    • 2
  1. 1.Department of Mathematics and StatisticsUniversity of Massachusetts (Emeritus)AmherstUSA
  2. 2.Department of Mathematics and Computer ScienceJuniata CollegeHuntingdonUSA

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