Description
This talk is about the $q$-Onsager algebra $O_q$. The algebra $O_q$ is defined by two generators and two relations called the $q$-Dolan/Grady relations. We will describe the finite-dimensional irreducible $O_q$-modules $V$ that satisfy a mild assumption. We will show that the $O_q$-generators act on $V$ as a tridiagonal pair. We will describe the tridiagonal pairs and the related tridiagonal systems, using the concept of a tetrahedron diagram. We will classify up to isomorphism the tridiagonal systems, and explain which ones come from an $O_q$-module.
Author
Paul Terwilliger
(U. Wisconsin-Madison Department of Mathematics)