The nonstandard deformation \(U_q'(so_n)\) for \(q\) a root of unity (Q2722111)

The authors 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 \(U_q'(so_n)\) for the case, where \(q^p=1\), are given. Representations of the main class act on a space of the dimension \(p^N\) (where \(N\) is the 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.