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The fixed-point-space dimension function for a finite group representation


Author: I. Martin Isaacs
Journal: Proc. Amer. Math. Soc. 107 (1989), 867-872
MSC: Primary 20C15
DOI: https://doi.org/10.1090/S0002-9939-1989-0982403-5
MathSciNet review: 982403
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Abstract: Given a complex representation of a finite group $ G$, construct the integer valued function $ \alpha $ on $ G$ by setting $ \alpha (g)$ to be the dimension of the fixed-point-space of $ g$ in the module corresponding to the given representation. Usually, $ \alpha $ is not a generalized character of $ G$ and for trivial reasons $ \vert G\vert\alpha $ is always a generalized character. The main result of this paper is that $ e\alpha $ is always a generalized character, where $ e$ is the exponent of $ G$.


References [Enhancements On Off] (What's this?)

  • [1] I. Martin Isaacs, Character theory of finite groups, Academic Press [Harcourt Brace Jovanovich, Publishers], New York-London, 1976. Pure and Applied Mathematics, No. 69. MR 0460423

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DOI: https://doi.org/10.1090/S0002-9939-1989-0982403-5
Article copyright: © Copyright 1989 American Mathematical Society