## Abstract

Let F denote a field. Fix a nonzero q∈F with q^{4}≠1. Let H_{q} denote a unital associative F-algebra generated by A, B, C and the relations assert that each of [Formula presented]+A,qCA−q^{−1}AC,[Formula presented]+C commutes with A, B, C. We call H_{q} the universal q-Hahn algebra. Motivated by the Clebsch–Gordan coefficients of U_{q}(sl_{2}), we find a homomorphism ♭:H_{q}→U_{q}(sl_{2})⊗U_{q}(sl_{2}). We show that the kernel of ♭ 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 U_{q}(sl_{2})-modules into the direct sums of finite-dimensional irreducible H_{q}-modules are also given in the paper.

Original language | English |
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Pages (from-to) | 61-90 |

Number of pages | 30 |

Journal | Journal of Algebra |

Volume | 496 |

DOIs | |

State | Published - 15 Feb 2018 |

## Keywords

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

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