Howe Duality and Algebras of the Askey–Wilson Type: An Overview

DOI10.1007/978-3-030-55777-5_21zbMath1492.17015arXiv1911.08314OpenAlexW2990320693MaRDI QIDQ5011795

Stéphane Vinet, Luc Vinet, Julien Gaboriaud

Publication date: 27 August 2021

Published in: Quantum Theory and Symmetries (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1911.08314

zbMATH Keywords

reductive dual pairscommutantsHowe dualityRacah, Bannai-Ito and Askey-Wilson algebras

Mathematics Subject Classification ID

Quantum groups (quantized enveloping algebras) and related deformations (17B37) Finite-dimensional groups and algebras motivated by physics and their representations (81R05) Superalgebras (17A70) Basic orthogonal polynomials and functions (Askey-Wilson polynomials, etc.) (33D45) Orthogonal polynomials and functions associated with root systems (33C52) Ring-theoretic aspects of quantum groups (16T20) Quadratic algebras (but not quadratic Jordan algebras) (17A45)

Cites Work

• The \(\mathbb{Z}_2^n\) Dirac-Dunkl operator and a higher rank Bannai-Ito algebra
• Superintegrability in two dimensions and the Racah-Wilson algebra
• The Higgs and Hahn algebras from a Howe duality perspective
• The dual pair \(Pin(2n) \times \mathfrak{osp}(1|2)\), the Dirac equation and the Bannai-Ito algebra
• The \(q\)-Higgs and Askey-Wilson algebras
• The higher rank \(q\)-deformed Bannai-Ito and Askey-Wilson algebra
• The dual pair (Uq(su(1,1)),oq1/2(2n)), q-oscillators, and Askey-Wilson algebras
• A higher rank Racah algebra and the $\mathbb{Z}_2^n$ Laplace–Dunkl operator
• The Racah algebra as a commutant and Howe duality

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