Degrees of irreducible representations are the same for all splitting fields

From Groupprops
Jump to: navigation, search

Statement

Suppose G is a finite group. Then, given any splitting field K for G (so the characteristic of K does not divide the order of G) it is possible to construct a bijection between the irreducible representations of G over K and the irreducible representations of G over the field of complex numbers, such that the bijection preserves the degree of a representation.

In particular, this means that the Degrees of irreducible representations (?) for a finite group are the same for all splitting fields (characteristic not dividing the group order).