Abstract
It is shown that the main result of N. R. Wallach, Principal orbit type theorems for reductive algebraic group actions and the Kempf–Ness Theorem, arXiv:1811.07195v1 (17 Nov 2018), is a special case of a more general statement, which can be deduced, using a short argument, from the classical Richardson and Luna theorems.
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References
N. R. Wallach, “Principal orbit type theorems for reductive algebraic group actions and the Kempf-Ness Theorem,” arXiv:1811.07195v1 (17 Nov 2018).
A. Borel, Linear Algebraic Groups, 2nd ed., in Graduate Texts in Math. (Springer, New York, 1991), Vol. 126.
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R. W. Richardson, “Principal orbit types for algebraic transformation spaces in characteristic zero,” Invent. math. 16, 6–14 (1972).
D. Luna, “Slices étales,” Bull. Soc. Math. de France 33, 81–105 (1973).
V. L. Popov, “Stability criteria for the action of a semisimple group on a factorial manifold,” Math. USSR Izv. 4 (3), 527–535 (1970).
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Popov, V.L. On Conjugacy of Stabilizers of Reductive Group Actions. Math Notes 105, 580–581 (2019). https://doi.org/10.1134/S0001434619030301
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DOI: https://doi.org/10.1134/S0001434619030301