 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-2-of-the-natural-sciences-course-of-the-university-of-cambridge/2004/paper-2/10/i/solution

The trace is invariant under a similarity transformation, by cyclicity of the trace:

χ_{D} (g) = tr (S D (g) S^{- 1}) = tr (D (g) S^{- 1} S) = χ_{D} (g) .

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