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## Irreducible linear representation

, 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]], $\mathbb{C}$ (the field of complex numbers) and $\overline{\mathbb{Q}}$ 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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