The \(\mathbb{Z}_2^n\) Dirac-Dunkl operator and a higher rank Bannai-Ito algebra

DOI10.1016/j.aim.2016.08.007zbMath1348.81253arXiv1511.02177OpenAlexW2517723927MaRDI QIDQ323678

Vincent X. Genest, Hendrik De Bie, Luc Vinet

Publication date: 10 October 2016

Published in: Advances in Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1511.02177

zbMATH Keywords

Dirac operatorDunkl operatorBannai-Ito algebra

Mathematics Subject Classification ID

Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) Reflection and Coxeter groups (group-theoretic aspects) (20F55) Infinite-dimensional groups and algebras motivated by physics, including Virasoro, Kac-Moody, (W)-algebras and other current algebras and their representations (81R10) Groups and algebras in quantum theory and relations with integrable systems (81R12) Applications of group representations to physics and other areas of science (20C35) Special quantum systems, such as solvable systems (81Q80)

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Cites Work

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• A Dirac-Dunkl equation on \(S^2\) and the Bannai-Ito algebra
• Bispectrality of the complementary Bannai-Itō polynomials
• Dunkl shift operators and Bannai-Ito polynomials
• The Howe duality for the Dunkl version of the Dirac operator
• Fourier transforms related to a root system of rank 1
• Multivariable Wilson polynomials and degenerate Hecke algebras
• \(q\)-deformed orthogonal and pseudo-orthogonal algebras and their representations
• 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
• A remark on the Casimir elements of Lie superalgebras and quantized Lie superalgebras
• 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

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