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Incoming links: Triviality of finite-dimensional unitary representations of SL2R
Past exam of the mathematics course of the University of Cambridge 2001 iii Paper 1 2 b iv Solution Created 2026-10-03 Updated 2026-10-14
Every unitary matrix is unitarily diagonalizable. Part (ii) therefore proves the stronger matrix statement , not merely a statement about its eigenvalues. The kernel of a group homomorphism is a normal subgroup, and it contains every upper unipotent. By part (iii) their normal closure is the entire group. ThusThis proves the triviality of finite-dimensional unitary representations of SL2R. In fact the argument used only the algebraic homomorphism property and finite-dimensional unitarity; it did not need continuity.