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

Research output: Contribution to journalArticlepeer-review

3 Scopus citations


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.

Original languageEnglish
Pages (from-to)61-90
Number of pages30
JournalJournal of Algebra
StatePublished - 15 Feb 2018


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


Dive into the research topics of 'An algebra behind the Clebsch–Gordan coefficients of Uq(sl2)'. Together they form a unique fingerprint.

Cite this