English

Little and Big $q-$Jacobi Polynomials and the Askey-Wilson algebra

Quantum Algebra 2019-04-03 v2

Abstract

The little and big q-Jacobi polynomials are shown to arise as basis vectors for representations of the Askey-Wilson algebra. The operators that these polynomials respectively diagonalize are identified within the Askey-Wilson algebra generated by twisted primitive elements of Uq(sl(2))\mathfrak U_q(sl(2)). The little q-Jacobi operator and a tridiagonalization of it are shown to realize the equitable embedding of the Askey-Wilson algebra into Uq(sl(2))\mathfrak U_q(sl(2)).

Keywords

Cite

@article{arxiv.1806.02656,
  title  = {Little and Big $q-$Jacobi Polynomials and the Askey-Wilson algebra},
  author = {Pascal Baseilhac and Xavier Martin and Luc Vinet and Alexei Zhedanov},
  journal= {arXiv preprint arXiv:1806.02656},
  year   = {2019}
}

Comments

v2: References added. 15 pp