Haar measure on E_q(2)

Abstract

The quantum E(2) group is one of the simplest known examples so far of a locally compact noncompact quantum group. The existence and uniqueness of an 'invariant measure' on this group has been proved in this article. Using the invariant measure, we compute certain orthogonality relations, which then tells us that any unitary representation can have both square-integrable and non square-integrable matrix entries.