An algebra behind the Clebsch-Gordan coefficients of U-q(sl(2))+/-

作者：Huang Hau Wen^*

来源：Journal of Algebra, 2018, 496: 61-90.

DOI：10.1016/j.jalgebra.2017.11.014

• Clebsch-Gordan coefficients
• q-Hahn polynomials
• Quantum algebras

Let IF denote a field. Fix a nonzero q is an element of F with q(4) not equal 1. Let H-q denote a unital associative F-algebra generated by A, B, C and the relations assert that each of
qBC - q(-1)CB/q(2) - q(-2) +A, qCA - q(-1) AC, qAB - q(-1)BA/q(2) - q(-2) + C
commutes with A, B, C. We call H-q the universal q-Hahn algebra. Motivated by the Clebsch-Gordan coefficients of Uq(sl(2)), we find a homomorphism b : H-q -> U-q(sl(2)) circle times U-q(sl(2)). We show that the kernel of b is an ideal of H-q generated by a central element of H-q. The decomposition formulae for the tensor products of irreducible Verma U-q(sl(2))-modules and of finite-dimensional irreducible Ug(sl(2))-modules into the direct sums of finite-dimensional irreducible H-q-modules are also given in the paper.

• 出版日期2018-2-15
• 单位中央民族大学