Askey-Wilson polynomials and the quantum SU(2) group: Survey and applications

被引：0
|
作者：
Koelink, HT [1 ]
机构：
[1] KATHOLIEKE UNIV LEUVEN,DEPT WISKUNDE,B-3001 LOUVAIN,HEVERLEE,BELGIUM
来源：
ACTA APPLICANDAE MATHEMATICAE | 1996年 / 44卷 / 03期
关键词：
group; SU(2); Askey-Wilson polynomials; representation theory; matrix elements; dual q-Krawtchouk polynomials; spherical and associated spherical elements; continuous q-ultraspherical polynomials; q-Hahn polynomials; characters; Chebyshev polynomials;
D O I：
暂无
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
Generalised matrix elements of the irreducible representations of the quantum SU(2) group are defined using certain orthonormal bases of the representation space. The generalised matrix elements are relatively infinitesimal invariant with respect to Lie algebra like elements of the quantised universal enveloping algebra of sl(2). A full proof of the theorem announced by Noumi and Mimachi [Proc. Japan Acad. Sci. Sei: A 66 (1990), 146-149] describing the generalised matrix elements in terms of the full four-parameter family of Askey-Wilson polynomials is given. Various known and new applications of this interpretation are presented.
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页码：295 / 352
页数：58
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