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A higher rank Racah algebra and the Z(2)(n) Laplace–Dunkl operator

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Abstract
A higher rank generalization of the (rank one) Racah algebra is obtained as the symmetry algebra of the Laplace–Dunkl operator associated to the $\mathbb{Z}_2^n$ root system. This algebra is also the invariance algebra of the generic superintegrable model on the n-sphere. Bases of Dunkl harmonics are constructed explicitly using a Cauchy–Kovalevskaia theorem. These bases consist of joint eigenfunctions of labelling Abelian subalgebras of the higher rank Racah algebra. A method to obtain expressions for both the connection coefficients between these bases and the action of the symmetries on these bases is presented.

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Chicago
De Bie, Hendrik, Vincent X Genest, Wouter van de Vijver, and Luc Vinet. 2018. “A Higher Rank Racah Algebra and the Z(2)(n) Laplace–Dunkl Operator.” Journal of Physics A-mathematical and Theoretical  51 (2).
APA
De Bie, H., Genest, V. X., van de Vijver, W., & Vinet, L. (2018). A higher rank Racah algebra and the Z(2)(n) Laplace–Dunkl operator. JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL  , 51(2).
Vancouver
1.
De Bie H, Genest VX, van de Vijver W, Vinet L. A higher rank Racah algebra and the Z(2)(n) Laplace–Dunkl operator. JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL  . TEMPLE CIRCUS, TEMPLE WAY, BRISTOL BS1 6BE, ENGLAND: IOP Publishing; 2018;51(2).
MLA
De Bie, Hendrik et al. “A Higher Rank Racah Algebra and the Z(2)(n) Laplace–Dunkl Operator.” JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL  51.2 (2018): n. pag. Print.
@article{8551474,
  abstract     = {A higher rank generalization of the (rank one) Racah algebra is obtained as the symmetry algebra of the Laplace--Dunkl operator associated to the \${\textbackslash}mathbb\{Z\}\_2\^{ }n\$  root system. This algebra is also the invariance algebra of the generic superintegrable model on the n-sphere. Bases of Dunkl harmonics are constructed explicitly using a Cauchy--Kovalevskaia theorem. These bases consist of joint eigenfunctions of labelling Abelian subalgebras of the higher rank Racah algebra. A method to obtain expressions for both the connection coefficients between these bases and the action of the symmetries on these bases is presented.},
  articleno    = {025203},
  author       = {De Bie, Hendrik and Genest, Vincent X and van de Vijver, Wouter and Vinet, Luc},
  issn         = {1751-8113},
  journal      = {JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL      },
  language     = {eng},
  number       = {2},
  pages        = {20},
  publisher    = {IOP Publishing},
  title        = {A higher rank Racah algebra and the Z(2)(n) Laplace--Dunkl operator},
  url          = {http://dx.doi.org/10.1088/1751-8121/aa9756},
  volume       = {51},
  year         = {2018},
}

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