Representations of Discrete Groups and Special Functions of Discrete Argument
Representations of Discrete Groups and Special Functions of Discrete Argument
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离散群的表示和离散参数的特殊函数
DOI：
10.1007/978-94-017-2883-6_5
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发表时间：
1993
影响因子：
1.7
通讯作者：
A. Klimyk
中科院分区：
文献类型：
--
作者：
N. J. Vilenkin;A. Klimyk
第六章和第八章研究了Krawtchouk多项式和Hahn多项式与群SU（2）和SL（2，n）的表示的关系，表示的矩阵元素作为行数的函数，Clebsch-Gordan系数分别用Krawtchouk多项式和Hahn多项式表示。但这些多项式与群表示理论还有另一种联系，即与对称群Sn和圈对称群S（n + 1，k）的不可约表示有关，这些表示关于相应子群的球函数用Krawtchouk和Hahn多项式表示。
In Chapters 6 and 8 we have studied connections of Krawtchouk and Hahn polynomials with representations of the groups SU(2) and SL(2,ℝ).Matrix elements of representations, considered as functions of row number, and Clebsch-Gordan coefficients are expressed respectively in terms of Krawtchouk and Hahn polynomials. But there is another connection of these polynomials with the theory of group representations, namely, with irreducible representations of the symmetric group S n and of the wreath symmetric group S(n + 1, k).Spherical functions of these representations with respect to corresponding subgroups are expressed in terms of Krawtchouk and Hahn polynomials.