On the Clebsch-Gordan coefficients for the quantum group Uq(2)

被引:0
|
作者
Guin, Satyajit [1 ]
Saurabh, Bipul [2 ]
机构
[1] Indian Inst Technol Kanpur, Dept Math & Stat, Kanpur 208016, India
[2] Indian Inst Technol Gandhinagar, Gandhinagar 382424, India
来源
PROCEEDINGS OF THE INDIAN ACADEMY OF SCIENCES-MATHEMATICAL SCIENCES | 2023年 / 133卷 / 02期
关键词
Compact quantum group; quantum unitary group; Clebsch-Gordan coefficients; POINCARE-DUALITY; REPRESENTATIONS;
D O I
10.1007/s12044-023-00762-2
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
We consider the compact quantum group U-q(2) for q is an element of C \ {0} with |q| not equal 1, and decompose the tensor product of two irreducible representations into irreducible components. The decomposition is realized in terms of a basis of homogeneous polynomials in four variables involving the matrix elements of the irreducible representations of U-q (2). Then, we compute the Clebsch-Gordan coefficients in terms of the q-hypergeometric series 3 phi(2). When q is real, the Clebsch-Gordan coefficients are real and its expression can be written in terms of the q-Hahn polynomial Q(n)(x; a, b, N|q(2)).
引用
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页数:20
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