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

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

doi:10.1016/0022-1236(91)90045-7

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

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

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

77 Citations (Scopus)

Abstract

In this paper, we study the finite dimensional unitary representations of the quantum group SU_q(2). Then we obtain the Peter-Weyl theorem for SU_q(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 SU_q(2).

Original language	English
Pages (from-to)	357-386
Number of pages	30
Journal	Journal of Functional Analysis
Volume	99
Issue number	2
DOIs	https://doi.org/10.1016/0022-1236(91)90045-7
Publication status	Published - 1991 Aug 1

ASJC Scopus subject areas

Analysis

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10.1016/0022-1236(91)90045-7

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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).",

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AU - Mimachi, Katsuhisa

AU - Nakagami, Yoshiomi

AU - Noumi, Masatoshi

AU - Ueno, Kimio

PY - 1991/8/1

Y1 - 1991/8/1

N2 - 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).

AB - 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).

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

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