Representations of the quantum group SUq(2) and the little q-Jacobi polynomials

Tetsuya Masuda, Katsuhisa Mimachi, Yoshiomi Nakagami, Masatoshi Noumi, Kimio Ueno

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    Abstract

    In this paper, we study the finite dimensional unitary representations of the quantum group SUq(2). Then we obtain the Peter-Weyl theorem for SUq(2) and the matrix elements of these unitary representations are explicitly expressed in terms of the little q-Jacobi polynomials which are known as q-analogues of orthogonal polynomials. Using these expressions, the orthogonality relations of these polynomials are obtained in terms of the Haar measure on the quantum group SUq(2).

    Original languageEnglish
    Pages (from-to)357-386
    Number of pages30
    JournalJournal of Functional Analysis
    Volume99
    Issue number2
    DOIs
    Publication statusPublished - 1991 Aug 1

    Fingerprint

    Jacobi Polynomials
    Unitary Representation
    Quantum Groups
    Weyl's Theorem
    Orthogonality Relations
    Haar Measure
    Q-analogue
    Orthogonal Polynomials
    Polynomial

    ASJC Scopus subject areas

    • Analysis

    Cite this

    Representations of the quantum group SUq(2) and the little q-Jacobi polynomials. / Masuda, Tetsuya; Mimachi, Katsuhisa; Nakagami, Yoshiomi; Noumi, Masatoshi; Ueno, Kimio.

    In: Journal of Functional Analysis, Vol. 99, No. 2, 01.08.1991, p. 357-386.

    Research output: Contribution to journalArticle

    Masuda, Tetsuya ; Mimachi, Katsuhisa ; Nakagami, Yoshiomi ; Noumi, Masatoshi ; Ueno, Kimio. / Representations of the quantum group SUq(2) and the little q-Jacobi polynomials. In: Journal of Functional Analysis. 1991 ; Vol. 99, No. 2. pp. 357-386.
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