Abstract
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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© 2000 Springer Science+Business Media Dordrecht
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Foulis, D.J., Wilce, A. (2000). Free Extensions of Group Actions, Induced Representations, and the Foundations of Physics. In: Coecke, B., Moore, D., Wilce, A. (eds) Current Research in Operational Quantum Logic. Fundamental Theories of Physics, vol 111. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-1201-9_6
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DOI: https://doi.org/10.1007/978-94-017-1201-9_6
Publisher Name: Springer, Dordrecht
Print ISBN: 978-90-481-5437-1
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