On representations of the Heisenberg relations for the quantumE(2) group

All irreducible^* -representations of the involutive algebraA generated by the so-called Heisenberg relations for the quantum deformation of the group of motions of the Euclidean plane are described.Dedicated to the 70th birthday of our teacher, Prof. Yu. M. BerezanskiiPublished in Ukrainskii Matematicheskii Zhurnal, Vol. 47, No. 5, pp. 689–692, May, 1995.This research was partially supported by the Ukrainian State Committee on Science and Technology, the International Science Foundation, grant No. U6D000, and a grant from the American Mathematical Society.