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 Cet article a éte moissonné depuis la source Math-Net.Ru

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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},
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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/

[1] Styrt O. G., “O prostranstve orbit kompaktnoi lineinoi gruppy Li s kommutativnoi svyaznoi komponentoi”, Tr. MMO, 70, 2009, 235–287 | MR | Zbl

[2] Styrt O. G., “O prostranstve orbit trekhmernoi kompaktnoi lineinoi gruppy Li”, Izv. RAN. Ser. matem., 75:4 (2011), 165–188 | DOI | MR | Zbl

[3] Vinberg E. B., Onischik A. L., Seminar po gruppam Li i algebraicheskim gruppam, URSS, M., 1995 | MR | Zbl

[4] Elashvili A. G., “Kanonicheskii vid i statsionarnye podalgebry tochek obschego polozheniya dlya prostykh lineinykh grupp Li”, Funkts. analiz i ego pril., 6:1 (1972), 51–62 | Zbl

[5] Styrt O. G., “O prosteishikh statsionarnykh podalgebrakh dlya kompaktnykh lineinykh algebr Li”, Tr. MMO, 73, no. 1, 2012, 133–150 | Zbl

[6] Dadok J., Kac V., “Polar representations”, J. Algebra, 92:2 (1985), 504–524 | DOI | MR | Zbl

[7] Rashevskii P. K., “Teorema o svyaznosti podgruppy odnosvyaznoi gruppy Li, perestanovochnoi s kakim-libo ee avtomorfizmom”, Tr. MMO, 30, 1974, 3–22

[8] Vinberg E. B., Popov V. L., “Teoriya invariantov”, Itogi nauki i tekhn. Ser. Sovrem. probl. matem., Fundam. napravleniya, 55, VINITI, M., 1989, 137–309 | MR

[9] Vinberg E. B., “Gruppa Veilya graduirovannoi algebry Li”, Izv. AN SSSR. Ser. matem., 40:3 (1976), 488–526 | MR | Zbl