On the conjugation action for quantum general linear groups.

We consider the conjugation action of a quantum group G over an arbitrary field k. In particular we consider the coordinate algebra k [ G (n) ] of the quantised general linear group G (n) , at an arbitrary non-zero parameter q , as a G (n) -module and give analogues of results of Kostant and Richardson. We also consider the case in which G is a product of quantum general linear groups and the problem of describing the conjugation invariants of k [ G ] for the action of a quantum subgroup. This is approached via finite dimensional sub-coalgebras of k [ G ] and the theory of quasi-hereditary algebras. [ABSTRACT FROM AUTHOR]