QDYBE: some explicit formulas for exchange matrix and related objects in case of sl(2), q=1

Abstract

This mainly tutorial paper is intended as a somewhat larger example for parts of the theory exposed in the Lectures on the dynamical Yang-Baxter equations by P. Etingof and O. Schiffmann, math.QA/9908064. We explicitly compute the matrix entries of the intertwining operator, fusion matrix and exchange matrix associated to sl(2,R) for q=1. We also consider the weighted trace function and the dual Macdonald-Ruijsenaars equation for this particular case. As expected, the matrix entries of the exchange matrix turn out to be Racah polynomials. However, the road to their explicit formula via the fusion matrix is quick, and it also yields an interesting way to derive their orthogonality relations.

19 pages

References in corpus (5)

• The Askey-scheme of hypergeometric orthogonal polynomials and its q-analogue
• Geometry and classification of solutions of the Classical Dynamical Yang-Baxter Equation
• Solutions of the quantum dynamical Yang-Baxter equation and dynamical quantum groups
• A Quasi-Hopf algebra interpretation of quantum 3-j and 6-j symbols and difference equations
• Exchange dynamical quantum groups

Cited by in corpus (1)

• Fusion and exchange matrices for quantized sl(2) and associated q-special functions