Nonclassical representations of the nonstandard deformations U'_q(so_n), U_q(iso_n) and U'_q(so_(n,1))

The aim of this paper is to announce the results on irreducible nonclassical type representations of the nonstandard q-deformations U'_q(so_n), U_q(iso_n) and U'_q(so_{n,1}) of the universal enveloping algebras of the Lie algebras so(n,C), iso_n and so_{n,1} when q is a real number (the algebra U'_q(so_{n,1}) is a real form of the algebra U'_q(so_{n+1})). These representations are characterized by the properties that they are singular at the point q=1.