Masuda, Tetsuya; Mimachi, Katsuhisa; Nakagami, Yoshiomi; Noumi, Masatoshi; Ueno, Kimio Representations of quantum groups and a q-analogue of orthogonal polynomials. (Représentations des groupes quantiques et un q-analogue des polynômes orthogonaux). (English) Zbl 0658.22010 C. R. Acad. Sci., Paris, Sér. I 307, No. 11, 559-564 (1988). A Peter-Weyl theorem is given for the Hopf algebra of the quantum group \(SL_ q(2)\). The corresponding matrix elements are expressed in terms of q-orthogonal polynomials and the action of the Casimir operator is explicited. Reviewer: G.Loupias Cited in 21 Documents MSC: 22E70 Applications of Lie groups to the sciences; explicit representations 81R10 Infinite-dimensional groups and algebras motivated by physics, including Virasoro, Kac-Moody, \(W\)-algebras and other current algebras and their representations 58H05 Pseudogroups and differentiable groupoids 16W30 Hopf algebras (associative rings and algebras) (MSC2000) 33C80 Connections of hypergeometric functions with groups and algebras, and related topics Keywords:Peter-Weyl theorem; Hopf algebra; quantum group; matrix elements; q- orthogonal polynomials; Casimir operator PDFBibTeX XMLCite \textit{T. Masuda} et al., C. R. Acad. Sci., Paris, Sér. I 307, No. 11, 559--564 (1988; Zbl 0658.22010)