Little and big q-Jacobi polynomials and the Askey-Wilson algebra

被引：4

作者：

Baseilhac, Pascal ^{[1
]}

Martin, Xavier ^{[1
]}

Vinet, Luc ^{[2
]}

Zhedanov, Alexei ^{[2
,3
]}

机构：

[1] Univ Orleans, Univ Tours, UMR 7013, Inst Denis Poisson,CNRS, Parc Grammt, F-37200 Tours, France

[2] Univ Montreal, Ctr Rech Math, CNRS, UMI 3457,Ctr Ville Stn, POB 6128, Montreal, PQ H3C 3J7, Canada

[3] Renmin Univ China, Informat Sch, Dept Math, Beijing 100872, Peoples R China

来源：

RAMANUJAN JOURNAL | 2020年 / 51卷 / 03期

关键词：

Askey-Wilson algebra; Tridiagonalization; Orthogonal polynomials; QUANTUM GROUP; REPRESENTATIONS;

D O I：

10.1007/s11139-018-0080-1

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The little and big q-Jacobi polynomials are shown to arise as basis vectors for representations of the Askey-Wilson algebra. The operators that these polynomials respectively diagonalize are identified within the Askey-Wilson algebra generated by twisted primitive elements of Uq(sl(2))The little q-Jacobi operator and a tridiagonalization of it are shown to realize the equitable embedding of the Askey-Wilson algebra into Uq(sl(2))

引用

页码：629 / 648

页数：20

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