International Journal of Mathematics and Mathematical Sciences
Volume 24 (2000), Issue 12, Pages 793-806

Some details of proofs of theorems related to the quantum dynamical Yang-Baxter equation

Tom H. Koornwinder

Korteweg-de Vries Institute, Universiteit van Amsterdam, Plantage Muidergracht 24, Amsterdam 1018 TV, The Netherlands

Received 7 July 2000

Copyright © 2000 Tom H. Koornwinder. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


This paper of tutorial nature gives some further details of proofs of some theorems related to the quantum dynamical Yang-Baxter equation. This mainly expands proofs given in “Lectures on the dynamical Yang-Baxter equation” by Etingof and Schiffmann, math.QA/9908064. This concerns the intertwining operator, the fusion matrix, the exchange matrix and the difference operators. The last part expands proofs given in “Traces of intertwiners for quantum groups and difference equations, I” by Etingof and Varchenko, math.QA/9907181. This concerns the dual Macdonald-Ruijsenaars equations.