The Universal Askey-Wilson Algebra and the Equitable Presentation of U q (sl 2 )

[摘要] ( this is shortened html-version of the paper's abstract ) Around 1992 A. Zhedanov introduced the Askey-Wilson algebra AW(3). Recently we introduced a central extension Δ of AW(3) called the universal Askey-Wilson algebra. In this paper we discuss a connection between Δ and the quantum algebra U q (sl 2 ). Our main result is an algebra injection from Δ into a relative of U q (sl 2 ); the relative is obtained from U q (sl 2 ) by adjoining three mutually commuting indeterminates. We describe the injection using the equitable presentation of U q (sl 2 ).

[关键词] Askey–Wilson relations;Leonard pair;Casimir element