An algebra behind the Clebsch–Gordan coefficients of Uq(sl2)

研究成果: 雜誌貢獻期刊論文同行評審

3 引文 斯高帕斯(Scopus)


Let F denote a field. Fix a nonzero q∈F with q4≠1. Let Hq denote a unital associative F-algebra generated by A, B, C and the relations assert that each of [Formula presented]+A,qCA−q−1AC,[Formula presented]+C commutes with A, B, C. We call Hq the universal q-Hahn algebra. Motivated by the Clebsch–Gordan coefficients of Uq(sl2), we find a homomorphism ♭:Hq→Uq(sl2)⊗Uq(sl2). We show that the kernel of ♭ is an ideal of Hq generated by a central element of Hq. The decomposition formulae for the tensor products of irreducible Verma Uq(sl2)-modules and of finite-dimensional irreducible Uq(sl2)-modules into the direct sums of finite-dimensional irreducible Hq-modules are also given in the paper.

頁(從 - 到)61-90
期刊Journal of Algebra
出版狀態已出版 - 15 2月 2018


深入研究「An algebra behind the Clebsch–Gordan coefficients of Uq(sl2)」主題。共同形成了獨特的指紋。