Rogers's \(q\)-ultraspherical polynomials on a quantum \(2\)-sphere

DOI10.1215/S0012-7094-91-06304-0zbMath0780.33011OpenAlexW1514569888MaRDI QIDQ1814228

Katsuhisa Mimachi, Masatoshi Noumi

Publication date: 25 June 1992

Published in: Duke Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1215/s0012-7094-91-06304-0

zbMATH Keywords

quantum groupq-ultraspherical polynomialsquantum 2-sphere

Mathematics Subject Classification ID

Quantum groups (quantized enveloping algebras) and related deformations (17B37) Basic orthogonal polynomials and functions (Askey-Wilson polynomials, etc.) (33D45) Connections of basic hypergeometric functions with quantum groups, Chevalley groups, (p)-adic groups, Hecke algebras, and related topics (33D80)

Related Items

Unnamed Item, Unnamed Item, Dirac operators on the quantum group SU(2) and the quantum sphere

Cites Work

• Quantum 2-spheres and big q-Jacobi polynomials
• Quantum spheres
• Representations of the quantum group \(SU_ q(2)\) and the little q-Jacobi polynomials
• Some basic hypergeometric orthogonal polynomials that generalize Jacobi polynomials
• Some q-Krawtchouk Polynomials on Chevalley Groups
• Über Orthogonalpolynome, die q‐Differenzengleichungen genügen
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