Stationary Subalgebras in General Position for Locally Strongly Effective Actions
Matematičeskie zametki, Tome 88 (2010) no. 5, pp. 689-707.

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In the present paper, a classification of all locally strongly effective actions of a semisimple algebraic group on a finite-dimensional complex vector space with nontrivial stationary subalgebra in general position is carried out.
Keywords: semisimple algebraic group, Lie algebra, locally strongly effective action, stationary subalgebra, reductive complex algebraic group, irreducible representation.
Mots-clés : Lie group
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D. G. Il'inskii. Stationary Subalgebras in General Position for Locally Strongly Effective Actions. Matematičeskie zametki, Tome 88 (2010) no. 5, pp. 689-707. http://geodesic.mathdoc.fr/item/MZM_2010_88_5_a5/

[1] E. B. Vinberg, V. L. Popov, “Teoriya invariantov”, Algebraicheskaya geometriya – 4, Itogi nauki i tekhn. Ser. Sovrem. probl. mat. Fundam. napravleniya, 55, VINITI, M., 1989, 137–309 | MR | Zbl

[2] D. Luna, R. W. Richardson, “A generalization of the Chevalley restriction theorem”, Duke Math. J., 46:3 (1979), 487–496 | DOI | MR | Zbl

[3] E. M. Andreev, E. B. Vinberg, A. G. Elashvili, “Orbity naibolshei razmernosti poluprostykh lineinykh grupp Li”, Funkts. analiz i ego pril., 1:4 (1967), 3–7 | MR | Zbl

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

[5] A. G. Elashvili, “Statsionarnye podalgebry tochek obschego polozheniya dlya neprivodimykh lineinykh grupp Li”, Funkts. analiz i ego pril., 6:2 (1972), 65–78 | MR | Zbl

[6] E. B. Vinberg, A. L. Onischik, Seminar po gruppam Li i algebraicheskim gruppam, Nauka, M., 1988 | MR | Zbl

[7] W. Fulton, J. Harris, Representation Theory. A First Course, Grad. Texts in Math., 129, Springer-Verlag, New York, 1991 | MR | Zbl