Bannai–Ito algebras and the osp(1;2) superalgebra

DOI10.1007/978-3-319-69164-0_52zbMath1390.17009arXiv1610.04797OpenAlexW2538221211MaRDI QIDQ4643479

Hendrik De Bie, Luc Vinet, Wouter van de Vijver, Vincent X. Genest

Publication date: 24 May 2018

Published in: Physical and Mathematical Aspects of Symmetries (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1610.04797

Mathematics Subject Classification ID

Applications of Lie (super)algebras to physics, etc. (17B81) Superalgebras (17A70) Subalgebras, congruence relations (08A30)

Related Items (7)

The Racah algebra: An overview and recent results ⋮ The dual pair \(Pin(2n) \times \mathfrak{osp}(1|2)\), the Dirac equation and the Bannai-Ito algebra ⋮ The space of Dunkl monogenics associated with \(\mathbb{Z}_2^3\) ⋮ The Racah algebra as a subalgebra of the Bannai-Ito algebra ⋮ Finite-dimensional modules of the universal Racah algebra and the universal additive DAHA of type \((C_1^\vee,C_1)\) ⋮ 𝔬𝔰𝔭(1,2) and generalized Bannai–Ito algebras ⋮ Convolution identities for Dunkl orthogonal polynomials from the osp(1|2) Lie superalgebra

Cites Work

• 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
• Dunkl shift operators and Bannai-Ito polynomials
• Deformed Heisenberg algebra, fractional spin fields, and supersymmetry without fermions
• A Laplace-Dunkl equation on \(S^2\) and the Bannai-Ito algebra
• The non-symmetric Wilson polynomials are the Bannai–Ito polynomials
• The Bannai–Ito algebra and a superintegrable system with reflections on the two-sphere
• The Bannai-Ito polynomials as Racah coefficients of the $sl_{-1}(2)$ algebra
• Do the Equations of Motion Determine the Quantum Mechanical Commutation Relations?
• A Note on the Quantum Rule of the Harmonic Oscillator

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