The universal DAHA of type \((C_1^\vee, C_1)\) and Leonard pairs of \(q\)-Racah type

DOI10.1016/j.laa.2017.07.014zbMath1371.33031arXiv1701.06089OpenAlexW2582194670MaRDI QIDQ2404963

Paul M. Terwilliger, Nomura, Kazumasa

Publication date: 21 September 2017

Published in: Linear Algebra and its Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1701.06089

zbMATH Keywords

Askey-Wilson polynomialtridiagonal pairLeonard pairDAHA

Mathematics Subject Classification ID

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 (10)

Finite-dimensional irreducible modules of the universal DAHA of type (C₁^∨,C₁) ⋮ Compatibility and companions for Leonard pairs ⋮ Unnamed Item ⋮ Near-bipartite Leonard pairs ⋮ Finite-dimensional irreducible modules of the universal Askey-Wilson algebra at roots of unity ⋮ Dual polar graphs, a nil-DAHA of rank one, and non-symmetric dual \(q\)-Krawtchouk polynomials ⋮ Finite-dimensional modules of the universal Askey-Wilson algebra and DAHA of type \((C_1^\vee ,C_1)\) ⋮ Double affine Hecke algebra of rank 1 and orthogonal polynomials on the unit circle ⋮ The universal DAHA of type (C1∨,C1) and Leonard triples ⋮ On the genus two skein algebra

Cites Work

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• Double affine Hecke algebras of rank 1 and the \(\mathbb Z_3\)-symmetric Askey-Wilson relations
• The classification of Leonard triples of QRacah type
• Linear transformations that are tridiagonal with respect to both eigenbases of a Leonard pair
• Zhedanov's algebra \(AW(3)\) and the double affine Hecke algebra in the rank one case. II. The spherical subalgebra
• Spin Leonard pairs
• The universal Askey-Wilson algebra and DAHA of type \((C_{1}^{\vee },C_{1})\)
• Raising and lowering operators for Askey-Wilson polynomials
• The relationship between Zhedanov's algebra \(AW(3)\) and the double affine Hecke algebra in the rank one case
• Two linear transformations each tridiagonal with respect to an eigenbasis of the other; the TD-D canonical form and the LB-UB canonical form
• LEONARD PAIRS AND THE ASKEY–WILSON RELATIONS
• Two linear transformations each tridiagonal with respect to an eigenbasis of the other

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