The dual pair \(Pin(2n) \times \mathfrak{osp}(1|2)\), the Dirac equation and the Bannai-Ito algebra

DOI10.1016/j.nuclphysb.2018.10.011zbMath1402.81132arXiv1810.00130OpenAlexW2897218430MaRDI QIDQ1626457

Alexei Zhedanov, Stéphane Vinet, Luc Vinet, Julien Gaboriaud

Publication date: 27 November 2018

Published in: Nuclear Physics. B (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1810.00130

Mathematics Subject Classification ID

Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) Applications of Lie (super)algebras to physics, etc. (17B81) Applications of Lie groups to the sciences; explicit representations (22E70) Superalgebras (17A70)

Related Items (7)

The Higgs and Hahn algebras from a Howe duality perspective ⋮ A Howe correspondence for the algebra of the \(\mathfrak{osp}(1 | 2)\) Clebsch-Gordan coefficients ⋮ Racah problems for the oscillator algebra, the Lie algebra \(\mathfrak{sl}_n\), and multivariate Krawtchouk polynomials ⋮ The dual pair (Uq(su(1,1)),oq1/2(2n)), q-oscillators, and Askey-Wilson algebras ⋮ The \(q\)-Higgs and Askey-Wilson algebras ⋮ Superintegrability and the dual \(- 1\) Hahn algebra in superconformal quantum mechanics ⋮ Howe Duality and Algebras of the Askey–Wilson Type: An Overview

Cites Work

• Unnamed Item
• Bôcher contractions of conformally superintegrable Laplace equations
• A Dirac-Dunkl equation on \(S^2\) and the Bannai-Ito algebra
• The \(\mathbb{Z}_2^n\) Dirac-Dunkl operator and a higher rank Bannai-Ito algebra
• Bôcher and abstract contractions of 2nd order quadratic algebras
• Dunkl shift operators and Bannai-Ito polynomials
• The Howe dual pair in Hermitean Clifford analysis
• ``Hidden symmetry of Askey-Wilson polynomials
• A Laplace-Dunkl equation on \(S^2\) and the Bannai-Ito algebra
• Embeddings of the Racah algebra into the Bannai-Itô algebra
• The non-symmetric Wilson polynomials are the Bannai–Ito polynomials
• Hypergeometric Orthogonal Polynomials and Their q-Analogues
• The Racah algebra as a commutant and Howe duality
• Bannai–Ito algebras and the osp(1;2) superalgebra
• The Bannai–Ito algebra and a superintegrable system with reflections on the two-sphere
• A superintegrable model with reflections onSⁿ⁻¹and the higher rank Bannai–Ito algebra

This page was built for publication: The dual pair \(Pin(2n) \times \mathfrak{osp}(1|2)\), the Dirac equation and the Bannai-Ito algebra