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Some Results on the Schur Index of a Representation of a Finite Group

Published online by Cambridge University Press:  20 November 2018

Charles Ford
Charles Ford*
Affiliation:
University of Toronto, Toronto, Ontario; Washington University, St. Louis, Missouri
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Let ℭ be a finite group with a representation as an irreducible group of linear transformations on a finite-dimensional complex vector space. Every choice of a basis for the space gives the representing transformations the form of a particular group of matrices. If for some choice of a basis the resulting group of matrices has entries which all lie in a subfield K of the complex field, we say that the representation can be realized in K. It is well known that every representation of ℭ can be realized in some algebraic number field, a finitedimensional extension of the rational field Q.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 22 , Issue 3 , 01 June 1970 , pp. 626 - 640
Copyright
Copyright © Canadian Mathematical Society 1970

References

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