Orbits for the adjoint coaction on quantum matrices
  Conjugation coactions of the quantum general linear group on the algebra of quantum matrices have been introduced in an earlier paper and the coinvariants have been determined. In this paper the notion of orbit is considered via co-orbit maps for these coactions. The co-orbit maps are calculated explicitly for 2 by 2 quantum matrices. In the NxN case we consider the case of a generic diagonal matrix when the deformation parameter is transcendental over the field generated by the diagonal entries. 
M. Domokos, R. Fioresi and T.H. Lenagan