The Nonstandard Deformation U'q(son) For q a Root of Unity
Abstract
We describe properties of the nonstandard q-deformation U'q(son) of the universal enveloping algebra U(son) of the Lie algebra son which does not coincide with the Drinfeld--Jimbo quantum algebra Uq(son). In particular, it is shown that there exists an isomorphism from U'q(son) to Uq(sln) and that finite dimensional irreducible representations of U'q(son) separate elements of this algebra. Irreducible representations of the algebras U'q(son) for q a root of unity qp=1 are given. The main class of these representations act on pN-dimensional linear space (where N is a number of positive roots of the Lie algebra son) and are given by r=dim son complex parameters. Some classes of degenerate irreducible representations are also described.
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