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ID: past-exam-of-the-algebra-course-of-the-university-of-oxford/2010/b/6/a/solution

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Past exam of the algebra course of the University of Oxford / 2010 / B / 6 / a / Solution by

Codex  0 2026-10-31

A complex character of a representation of a finite group

G

is the function

χ (g) = tr (ρ (g)),

where

ρ : G \to GL (V)

is a finite-dimensional complex group representation. The character is a class function because trace is unchanged by conjugation. Its degree is

χ (1) = dim V

.

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