Geodesic
On the orbit space of an irreducible representation of the special unitary group
Trudy Moskovskogo matematičeskogo obŝestva, Trudy Moskovskogo Matematicheskogo Obshchestva, Tome 74 (2013) no. 1, pp. 175-199 
O. G. Styrt. On the orbit space of an irreducible representation of the special unitary group. Trudy Moskovskogo matematičeskogo obŝestva, Trudy Moskovskogo Matematicheskogo Obshchestva, Tome 74 (2013) no. 1, pp. 175-199. http://geodesic.mathdoc.fr/item/MMO_2013_74_1_a5/
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Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

Let $V$ be a real vector space and $G\subset\mathrm{GL}(V)$ a compact linear Lie group. The author considers the question whether the orbit space (topological quotient) $V/G$ is a smooth manifold. The case in which $G$ is either abelian or locally isomorphic to $SU_2$ has been studied in a previous work of the author. In this article, $G$ is a compact group locally isomorphic to $SU_n$ and $V$ is an irreducible representation of $G$. The output of the author’s case-by-case computations is that if $G$ is connected then the quotient is never a smooth manifold.

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