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Communications in Mathematical Physics

, Volume 177, Issue 2, pp 399–415 | Cite as

Spectral analysis and the Haar functional on the quantumSU (2) group

  • H. T. Koelink
  • J. Verding
Article

Abstract

The Haar functional on the quantumSU(2) group is the analogue of invariant integration on the groupSU(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 quantumSU(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.

Keywords

Neural Network Statistical Physic Matrix Element Complex System Spectral Analysis 
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Copyright information

© Springer-Verlag 1996

Authors and Affiliations

  • H. T. Koelink
    • 1
  • J. Verding
    • 2
  1. 1.Vakgroep WiskundeUniversiteit van AmsterdamAmsterdamThe Netherlands
  2. 2.Departement WiskundeKatholieke Universiteit LeuvenLeuven (Heverlee)Belgium

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