Primitive Ideals of Cq(SL(n))

✍ Scribed by T.J. Hodges; T. Levasseur

• Publisher: Elsevier Science
• Year: 1994
• Tongue: English
• Weight: 484 KB
• Volume: 168
• Category: Article
• ISSN: 0021-8693
• DOI: 10.1006/jabr.1994.1239

✦ Synopsis

The primitive ideals of the quantum group (\mathbf{C}{q}[S L(n)]) are classified in the case where (q) is a non-zero complex number which is not a root of unity. It is shown that the orbits in Prim (\mathbf{C}{q}[S L(n)]) under the action of the character group (H \cong) (\left(\mathbf{C}^{*}\right)^{n-1}) are parameterized naturally by (W \times W) where (W) is the associated Weyl group. It is shown that there is a natural one-to-one correspondence between primitive ideals of (\mathbf{C}_{4}[S L(n)]) and symplectic leaves of the associated Poisson algebraic group (S L(n, \mathbf{C}) . \quad 1994) Academic Press. Inc.