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Irreducible linear representation

25 bytes added, 15:05, 1 August 2011
For finite groups over a splitting field
===For finite groups over a splitting field===
A [[splitting field]] is a field of characteristic not dividing the order of the group whereby the irreducible representations over that field remain irreducible in all bigger fields. We Over a splitting field, we have the following:
* [[Number of irreducible representations equals number of conjugacy classes]]
In addition, there are a number of other combinatorial and arithmetic controls on the nature and degrees of irreducible representations. For more, see [[degrees of irreducible representations]].
==Relation with other properties==
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