Nonclassical representations of the nonstandard deformations U'q(soₙ), Uq(isoₙ) and U'q(soₙ,₁)

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