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

We construct one and two variable models of the p, q-algebra epsilon p,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. (C) 2007 Elsevier Inc. All rights reserved.