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