Primitive ideals of \(\mathbb{C}_ q[SL(n)]\)
Let \(q\) be a nonzero complex number which is not a root of unity. The authors classify the primitive spectrum of the quantum group \(\mathbb{C}_ q [\text{SL} (n)]\), showing that there is a natural bijection between primitive ideals in this ring and symplectic leaves of the associated Poisson group \(\text{SL} (n, \mathbb{C})\). They also show that orbits of primitive ideals under a natural \(n-1\)-torus of automorphisms are parametrized by \(W\times W\), where \(W\) is the associated Weyl group, isomorphic to the symmetric group on \(n\) letters. This paper generalizes an earlier one of the authors which dealt with the case \(n=3\) [Commun. Math. Phys. 156, 581-605 (1993; Zbl 0801.17012)]. Many of the ideas and methods come from a paper of \textit{Ya. Soibelman} [Leningr. Math. J. 2, 161-178 (1991); translation from Algebra Anal. 2, 190-212 (1990; Zbl 0708.46029)]. The results have been generalized to quantum groups attached to arbitrary simply connected semisimple complex Lie groups by \textit{A. Joseph} [J. Algebra 169, 441-511 (1994; Zbl 0814.17013) see the following review; see also C. R. Acad. Sci., Paris, Sér. I 316, 1139-1142 (1993; Zbl 0784.17021)].
scientific article; zbMATH DE number 645090