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Harmonic analysis on the SU(2) dynamical quantum group

Erik Koelink·Hjalmar Rosengren
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Abstract

Dynamical quantum groups were recently introduced by Etingof and Varchenko as an algebraic framework for studying the dynamical Yang-Baxter equation, which is precisely the Yang-Baxter equation satisfied by 6j-symbols. We investigate one of the simplest examples, generalizing the standard SU(2) quantum group. The matrix elements for its corepresentations are identified with Askey-Wilson polynomials, and the Haar measure with the Askey-Wilson measure. The discrete orthogonality of the matrix elements yield the orthogonality of q-Racah polynomials (or quantum 6j-symbols). The Clebsch-Gordan coefficients for representations and corepresentations are also identified with q-Racah polynomials. This results in new algebraic proofs of the Biedenharn-Elliott identity satisfied by quantum 6j-symbols.

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Erik Koelink, Hjalmar Rosengren. 2001-05-17. Harmonic analysis on the SU(2) dynamical quantum group. https://arxiv.org/abs/math/0010093

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