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Published December 15, 2000 | public
Journal Article

On Primitive Linear Representations of Finite Groups

Abstract

Let F be a field, let G be a finite group, and let π be a linear representation of G over F; that is, π is a group homomorphism π: G → GL(V) of G into the general linear group on a finite-dimensional vector space V over F. We say π is AI if π is completely reducible and for each normal subgroup H of G, each irreducible FH-submodule of V is absolutely irreducible. For example, if F is algebraically closed then all completely reducible representations over F are AI. In particular, all of our theorems hold over the complex numbers without the hypothesis that the representation is AI.

Additional Information

© 2000 Academic Press. Received 12 April 2000. This work was partially supported by National Science Foundation grant NSF-9901367.

Additional details

Created:
August 19, 2023
Modified:
October 26, 2023