Haar measure on \(E_ q(2)\)
Existence and uniqueness of an invariant weight on the quantum \(E(2)\) group is proved. The proof uses the knowledge of the Haar state on the quantum \(\text{SU} (2)\) group and exploits the fact that this group is related to \(E_q (2)\) through a contraction procedure. All irreducible unitary representations are found and orthogonality relations between their matrix entries are computed. It is found that unlike for a classical locally compact group with a two-sided invariant measure, any unitary representation can have square-integrable as well as non square-integrable matrix entries, which brings to fore the basis dependent nature of this quantum group. (E-mail: arup\@isid.ernet.in).
scientific article; zbMATH DE number 950214