An attractive basis for the $q-$Onsager algebra

Abstract

Let $\text{A},{\text{A}}^{\ast }$ be the fundamental generators of the $q-$Onsager algebra. A linear basis for the $q-$Onsager algebra is known as the `zig-zag' basis [IT09]. In this letter, an attractive basis for the $q-$Onsager algebra is conjectured, based on the relation between the $q-$Onsager algebra and a quotient of the infinite dimensional algebra ${\mathcal{A}}_q$ introduced in [BK05].

14 pages

Cited by in corpus (8)

• The $q$-Onsager Algebra and the Universal Askey-Wilson Algebra
• Diagonalization of the Heun-Askey-Wilson operator, Leonard pairs and the algebraic Bethe ansatz
• The alternating presentation of $U_q(\widehat{g{l}_2})$ from Freidel-Maillet algebras
• FRT presentation of classical Askey-Wilson algebras
• An action of the free product ${\mathbb{Z}}_2\star {\mathbb{Z}}_2\star {\mathbb{Z}}_2$ on the $q$-Onsager algebra and its current algebra
• A conjecture concerning the $q$-Onsager algebra
• A compact presentation for the alternating central extension of the positive part of $U_q({\widehat{\mathfrak{sl}}}_2)$
• The $q$-Onsager algebra and its alternating central extension