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

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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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     author = {O. G. Styrt},
     title = {On the orbit space of an irreducible representation of the special unitary group},
     journal = {Trudy Moskovskogo matemati\v{c}eskogo ob\^{s}estva},
     pages = {175--199},
     publisher = {mathdoc},
     volume = {74},
     number = {1},
     year = {2013},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MMO_2013_74_1_a5/}
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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/