IntroductionLet g be a complex semi-simple Lie-Algebra and G its adjoint group. A sheet of g is a maximal irreducible subset of g consisting of G-orbits of a fixed dimension. The problem of a complete description of the orbit-space giG in geometrical terms (set-theoretically it has been done by Dynkin) splits naturally into two steps:1. To classify the sheets and to describe their intersections. 2. To parametrize the orbits in each sheet. The purpose of this paper is to work out general answers to both problems, the main purpose being problem 2. This is solved by using "almost regular" invariant functions on the sheet S. These are, by definition, those rational invariant functions on S, which are integral over the ring of regular invariant functions on the closure S.
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