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The Nonstandard Deformation U'_q(so_n) For q a Root of Unity

N. Z. Iorgov·A. U. Klimyk
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Abstract

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

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BibTeXRIS

N. Z. Iorgov, A. U. Klimyk. 2000-07-17. The Nonstandard Deformation U'_q(so_n) For q a Root of Unity. https://arxiv.org/abs/math/0007105

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