New realizations of algebras of the Askey-Wilson type in terms of Lie and quantum algebras

Nicolas Crampe, Dounia Shaaban Kabakibo, Luc Vinet

The Askey-Wilson algebra is realized in terms of the elements of the quantum algebras $U_q(\mathfrak{su}(2))$ or $U_q(\mathfrak{su}(1,1))$. A new realization of the Racah algebra i…