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.