On models of certain p, q-algebra representations: The quantum Euclidean algebra Ep,q(2)

We construct one and two variable models of the p, q-algebra Ep,q (2) in terms of ladder operators.We define two p, q-analogues of the exponential function mapping and using these show that matrix elements of these operators can be represented in terms of p, q-series. Further, we exhibit that these matrix elements satisfy certain biorthogonality relations. © 2007 Elsevier Inc. All rights reserved