Minimally irreducible linear representation: Difference between revisions
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==Definition== | ==Definition== | ||
A [[linear representation]] of a [[ | A finite-dimensional [[linear representation]] of a [[group]] is said to be '''minimally irreducible''' if its restriction to any proper subgroup is reducible. | ||
It turns out that the image of a group under a minimally irreducible linear representation must be a [[finite group]]. | |||
Latest revision as of 23:51, 7 May 2008
This article describes a property to be evaluated for a linear representation of a group, i.e. a homomorphism from the group to the general linear group of a vector space over a field
Definition
A finite-dimensional linear representation of a group is said to be minimally irreducible if its restriction to any proper subgroup is reducible.
It turns out that the image of a group under a minimally irreducible linear representation must be a finite group.