ORBITS OF LOW CODIMENSION ON IRREDUCIBLE REPRESENTATIONS OF SIMPLE ALGEBRAIC GROUPS

We classify irreducible representations of simple algebraic groups in arbitrary characteristic which have an orbit of low codimension. For each indecomposable root system X-n we give a polynomial function f which is cubic in n and we list all irreducible representations of the simply connected simple algebraic group G of type X-n which have an orbit of codimension less than or equal to f(X-n). For all these irreducible representations, we determine the codimension of the largest orbit or at least give narrow bounds for the codimension of such an orbit.