Spectral analysis and the Haar functional on the quantum SU(2) group

Details Spectral analysis and the Haar functional on the quantum SU(2) group Spectral analysis and the Haar functional on the quantum SU(2) group

1994-12-12

arxiv.org/abs/math/9412225v1

Mathematics

Quantum Algebra

Scientific paper

The Haar functional on the quantum $SU(2)$ group is the analogue of invariant integration on the group $SU(2)$. If restricted to a subalgebra generated by a self-adjoint element the Haar functional can be expressed as an integral with a continuous measure or with a discrete measure or by a combination of both. These results by Woronowicz and Koornwinder have been proved by using the corepresentation theory of the quantum $SU(2)$ group and Schur's orthogonality relations for matrix elements of irreducible unitary corepresentations. These results are proved here by using a spectral analysis of the generator of the subalgebra. The spectral measures can be described in terms of the orthogonality measures of orthogonal polynomials by using the theory of Jacobi matrices.

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