𝔬𝔰𝔭(1,2) and generalized Bannai–Ito algebras

DOI10.1090/tran/7733zbMath1482.17013arXiv1705.03761OpenAlexW2964243608MaRDI QIDQ5234484

Luc Vinet, Vincent X. Genest, Luc Lapointe

Publication date: 26 September 2019

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1705.03761

zbMATH Keywords

orthogonal polynomialssuperalgebrascommutantDunkl operatorsBannai-Ito polynomialsorthosymplectic Lie superalgebrasBannai-Ito algebrasAskey-Wilson

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) Simple, semisimple, reductive (super)algebras (17B20) Orthogonal polynomials and functions associated with root systems (33C52)

Related Items (4)

Finite-dimensional irreducible modules of the Bannai-Ito algebra at characteristic zero ⋮ The Racah algebra as a subalgebra of the Bannai-Ito algebra ⋮ Bannai-Ito algebras and the universal \(R\)-matrix of \(\mathfrak{osp}(1\!\!\mid\!\!2)\) ⋮ The q‐Bannai–Ito algebra and multivariate (−q)‐Racah and Bannai–Ito polynomials

Cites Work

• Unnamed Item
• Unnamed Item
• 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
• On the algebra of symmetries of Laplace and Dirac operators
• Dunkl shift operators and Bannai-Ito polynomials
• A new construction of Young's seminormal representation of the symmetric groups
• Symmetric polynomials and the center of the symmetric group ring
• A Laplace-Dunkl equation on \(S^2\) and the Bannai-Ito algebra
• The non-symmetric Wilson polynomials are the Bannai–Ito polynomials
• Dunkl operators and a family of realizations of $\mathfrak{osp}(1\vert2)$
• Differential-Difference Operators Associated to Reflection Groups
• Seminormal Representations of Weyl Groups and Iwahori-Hecke Algebras
• Symmetric functions andB_N-invariant spherical harmonics
• Rodrigues Formula for the Nonsymmetric Multivariable Laguerre Polynomial
• Bannai–Ito algebras and the osp(1;2) superalgebra
• 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

This page was built for publication: 𝔬𝔰𝔭(1,2) and generalized Bannai–Ito algebras