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Sur certaines représentations des groupes semi-simples. (French) Zbl 0538.14007
The author states (without proof) the following theorem: let G be a connected semi-simple complex algebraic group, U a maximal unipotent subgroup, and (p,V) a finite-dimensional representation of G; if \({\mathbb{C}}[V]^ U\) is isomorphic to a polynomial algebra, the closure of every G-orbit in V is a normal variety with rational singularities. A complete list of the representations having the preceding property when G is simple is given.
Reviewer: J.Oesterlé

14L24 Geometric invariant theory
14B05 Singularities in algebraic geometry
20G05 Representation theory for linear algebraic groups
14L30 Group actions on varieties or schemes (quotients)
20G20 Linear algebraic groups over the reals, the complexes, the quaternions
32M05 Complex Lie groups, group actions on complex spaces