Dualities in the q‐Askey Scheme and Degenerate DAHA

DOI10.1111/sapm.12229zbMath1408.33032arXiv1803.02775OpenAlexW3125424247MaRDI QIDQ4627034

Marta Mazzocco, Koornwinder, Tom H.

Publication date: 7 March 2019

Published in: Studies in Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1803.02775

Mathematics Subject Classification ID

Hecke algebras and their representations (20C08) Basic orthogonal polynomials and functions (Askey-Wilson polynomials, etc.) (33D45)

Related Items (12)

Charting the 𝑞-Askey scheme ⋮ Finite-dimensional irreducible modules of the universal DAHA of type (C₁^∨,C₁) ⋮ Grassmann graphs, degenerate DAHA, and non-symmetric dual \(q\)-Hahn polynomials ⋮ Charting the \(q\)-Askey scheme. II. The \(q\)-Zhedanov scheme ⋮ Unnamed Item ⋮ Finite-dimensional irreducible modules of the universal Askey-Wilson algebra at roots of unity ⋮ The Virasoro fusion kernel and Ruijsenaars' hypergeometric function ⋮ Sklyanin-like algebras for (q-)linear grids and (q-)para-Krawtchouk polynomials ⋮ Higher rank relations for the Askey-Wilson and \(q\)-Bannai-Ito algebra ⋮ Higher rank classical analogs of the Askey-Wilson algebra from the sl_N Onsager algebra ⋮ FRT presentation of classical Askey-Wilson algebras ⋮ The Askey–Wilson algebra and its avatars

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• The universal Askey-Wilson algebra
• Differential equations in the spectral parameter
• Finite-dimensional irreducible modules of the universal Askey-Wilson algebra
• Duality of \(q\)-polynomials, orthogonal on countable sets of points
• Fourier transforms related to a root system of rank 1
• Zhedanov's algebra \(AW(3)\) and the double affine Hecke algebra in the rank one case. II. The spherical subalgebra
• Collisions of Calogero-Moser particles and an adelic Grassmannian (with an appendix by I. G. Macdonald)
• ``Hidden symmetry of Askey-Wilson polynomials
• Differential equations in the spectral parameter, Darboux transformations and a hierarchy of master symmetries for KdV
• On the polynomial \(\tau\)-functions for the KP hierarchy and the bispectral property
• Dual isomonodromic deformations and moment maps to loop algebras
• Cherednik algebras and differential operators on quasi-invariants.
• Bilinear summation formulas from quantum algebra representations
• Nonsymmetric Koornwinder polynomials and duality
• Mutual integrability, quadratic algebras, and dynamical symmetry
• Bispectral KP solutions and linearization of Calogero-Moser particle systems
• Double affine Hecke algebra of rank 1 and orthogonal polynomials on the unit circle
• Non-symmetric basic hypergeometric polynomials and representation theory for confluent Cherednik algebras
• The relationship between Zhedanov's algebra \(AW(3)\) and the double affine Hecke algebra in the rank one case
• Confluences of the Painlevé equations, Cherednik algebras and q-Askey scheme
• The non-symmetric Wilson polynomials are the Bannai–Ito polynomials
• Nonsymmetric Askey–Wilson polynomials as vector-valued polynomials
• Bispectral commutative ordinary differential operators.
• The Analytic Theory of Matrix Orthogonal Polynomials
• Hypergeometric Orthogonal Polynomials and Their q-Analogues
• A Lie-theoretic construction of some representations of the degenerate affine and double affine Hecke algebras of type 𝐵𝐶_{𝑛}
• Some basic hypergeometric orthogonal polynomials that generalize Jacobi polynomials
• Differential-Difference Operators Associated to Reflection Groups
• Orthogonal Polynomials, Duality and Association Schemes
• Painlevé Monodromy Manifolds, Decorated Character Varieties, and Cluster Algebras
• Dual polar graphs, a nil-DAHA of rank one, and non-symmetric dual \(q\)-Krawtchouk polynomials

This page was built for publication: Dualities in the q‐Askey Scheme and Degenerate DAHA