Quotients for sheets of conjugacy classes

We provide a description of the orbit space of a sheet S for the conjugation action of a complex simple simply connected algebraic group G. This is obtained by means of a bijection between S∕G and the quotient of a shifted torus modulo the action of a subgroup of the Weyl group and it is the group analogue of a result due to Borho and Kraft. We also describe the normalisation of the categorical quotient // for arbitrary simple G and give a necessary and sufficient condition for //G to be normal in analogy to results of Borho, Kraft and Richardson. The example of G2 is worked out in detail.