The Z2n Dirac-Dunkl operator and a higher rank Bannai-Ito algebra

被引：28

作者：

De Bie, Hendrik ^{[1
]}

Genest, Vincent X. ^{[2
]}

Vinet, Luc ^{[3
]}

机构：

[1] Univ Ghent, Fac Engn & Architecture, Dept Math Anal, Galglaan 2, B-9000 Ghent, Belgium

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

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

来源：

ADVANCES IN MATHEMATICS | 2016年 / 303卷

基金：

加拿大自然科学与工程研究理事会;

关键词：

Dirac operator; Dunkl operator; Bannai-Ito algebra;

D O I：

10.1016/j.aim.2016.08.007

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The kernel of the Z(2)(n) Dirac-Dunkl operator is examined. The symmetry algebra A(n) of the associated Dirac-Dunkl equation on Sn-1 is determined and is seen to correspond to a higher rank generalization of the Bannai-Ito algebra. A basis for the polynomial null-solutions of the Dirac-Dunkl operator is constructed. The basis elements are joint eigenfunctions of a maximal commutative subalgebra of An and are given explicitly in terms of Jacobi polynomials. The symmetry algebra is shown to act irreducibly on this basis via raising/lowering operators. A scalar realisation of An is proposed. (C) 2016 Elsevier Inc. All rights reserved.

引用

页码：390 / 414

页数：25

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