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Irreducible linear representation

152 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. For a [[finite group]], <math>\mathbb{C}</math> (the field of complex numbers) and <math>\overline{\mathbb{Q}}</math> are examples of splitting fields. Over a splitting field, we have the following:
* [[Number of irreducible representations equals number of conjugacy classes]]
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