A higher rank Racah algebra and the Z2n Laplace-Dunkl operator

被引：31

作者：

De Bie, Hendrik ^{[1
]}

Genest, Vincent X. ^{[2
]}

van de Vijver, Wouter ^{[1
]}

Vinet, Luc ^{[3
]}

机构：

[1] Univ Ghent, Fac Engn & Architecture, Dept Math Anal, Krijgslaan 281, B-9000 Ghent, Belgium

[2] MIT, Dept Math, 77 Massachusetts Ave, Cambridge, MA 02139 USA

[3] Univ Montreal, Ctr Rech Math, POB 6128,Ctr Ville Stn, Montreal, PQ H3C 3J7, Canada

来源：

JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL | 2018年 / 51卷 / 02期

基金：

加拿大自然科学与工程研究理事会;

关键词：

Racah algebra; Dunkl operators; integrable systems; connection coefficients; SUPERINTEGRABLE SYSTEM; POLYNOMIALS;

D O I：

10.1088/1751-8121/aa9756

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

A higher rank generalization of the (rank one) Racah algebra is obtained as the symmetry algebra of the Laplace-Dunkl operator associated to the 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.

引用

页数：20

共 31 条

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