The universal DAHA of type (C1∨,C1) and Leonard triples

DOI10.1080/00927872.2020.1832105zbMath1480.16058arXiv2005.02386OpenAlexW3094362006MaRDI QIDQ5856293

Hau-Wen Huang

Publication date: 25 March 2021

Published in: Communications in Algebra (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2005.02386

zbMATH Keywords

double affine Hecke algebrasLeonard triplesLeonard pairsAskey-Wilson algebras

Mathematics Subject Classification ID

Representations of orders, lattices, algebras over commutative rings (16G30) Infinite-dimensional groups and algebras motivated by physics, including Virasoro, Kac-Moody, (W)-algebras and other current algebras and their representations (81R10) 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) Associative rings and algebras arising under various constructions (16S99)

Related Items (3)

Compatibility and companions for Leonard pairs ⋮ Near-bipartite Leonard pairs ⋮ Finite-dimensional modules of the universal Askey-Wilson algebra and DAHA of type \((C_1^\vee ,C_1)\)

Cites Work

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• The universal Askey-Wilson algebra
• Double affine Hecke algebras of rank 1 and the \(\mathbb Z_3\)-symmetric Askey-Wilson relations
• The classification of Leonard triples of QRacah type
• Finite-dimensional irreducible modules of the universal Askey-Wilson algebra
• Modular Leonard triples
• Zhedanov's algebra \(AW(3)\) and the double affine Hecke algebra in the rank one case. II. The spherical subalgebra
• ``Hidden symmetry of Askey-Wilson polynomials
• Double affine Hecke algebras and Macdonald's conjectures
• The universal DAHA of type \((C_1^\vee, C_1)\) and Leonard pairs of \(q\)-Racah type
• 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
• Orthogonal Polynomials, Duality and Association Schemes
• LEONARD PAIRS AND THE ASKEY–WILSON RELATIONS
• Two linear transformations each tridiagonal with respect to an eigenbasis of the other

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