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Mathematics > Quantum Algebra

arXiv:math/0010093 (math)
[Submitted on 10 Oct 2000 (v1), last revised 17 May 2001 (this version, v2)]

Title:Harmonic analysis on the SU(2) dynamical quantum group

Authors: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.
Comments: 51 pages; minor corrections
Subjects: Quantum Algebra (math.QA); Classical Analysis and ODEs (math.CA)
MSC classes: 20G42, 33D45, 33D80
Cite as: arXiv:math/0010093 [math.QA]
  (or arXiv:math/0010093v2 [math.QA] for this version)
  https://doi.org/10.48550/arXiv.math/0010093
Journal reference: Acta Appl. Math. 69 (2001), 163-220

Submission history

From: Hjalmar Rosengren [view email]
[v1] Tue, 10 Oct 2000 11:55:41 UTC (46 KB)
[v2] Thu, 17 May 2001 09:12:47 UTC (45 KB)
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