Geodesic
On Conjugacy of Stabilizers of Reductive Group Actions
Matematičeskie zametki, Tome 105 (2019) no. 4, pp. 589-591 Cet article a éte moissonné depuis la source Math-Net.Ru

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It is shown that the main result of [1], is a special case of a more general statement, which can be deduced, using a short argument, from the classical Richardson and Luna theorems.
Keywords: reductive algebraic group, stabilizer
Mots-clés : action, conjugacy. 
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V. L. Popov. On Conjugacy of Stabilizers of Reductive Group Actions. Matematičeskie zametki, Tome 105 (2019) no. 4, pp. 589-591. http://geodesic.mathdoc.fr/item/MZM_2019_105_4_a8/

[1] N. R. Wallach, Principal Orbit Type Theorems for Reductive Algebraic Group Actions and the Kempf–Ness Theorem, 2018, arXiv: 1811.07195v1

[2] A. Borel, Linear Algebraic Groups, Springer, New York, 1991 | MR | Zbl

[3] V. L. Popov, E. B. Vinberg, “Invariant theory”, Algebraic Geometry IV, Encyclopaedia of Math. Sci., 55, Springer-Verlag, Berlin, 1994, 123–278 | DOI

[4] R. W. Richardson, “Principal orbit types for algebraic transformation spaces in characteristic zero”, Invent. Math., 16 (1972), 6–14 | DOI | MR | Zbl

[5] D. Luna, “Slices étales”, Bull. Soc. Math. France, 33 (1973), 81–105 | MR | Zbl

[6] V. L. Popov, “Kriterii stabilnosti deistviya poluprostoi gruppy na faktorialnom mnogoobrazii”, Izv. AN SSSR. Ser. matem., 34:3 (1970), 523–531 | MR | Zbl