Green function on the quantum plane

Abstract

Green function (which can be called the q-analogous of the Hankel function) on the quantum plane E 2 q = E q (2)/U(1) is constructed.

Unitary representations of the two-dimensional Euclidean group in the Heisenberg algebra

“…For example there exists an extensive literature on the q-deformed groups E q (2) and SU q (2) which are the automorphism groups of the quantum plane zz * = qz * z and the quantum sphere respectively [1]. Using group theoretical methods the invariant distance and the Green functions have also been written in these deformed spaces [2].…”