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 Izv. Akad. Nauk SSSR Ser. Mat., 1984, Volume 48, Issue 2, Pages 411–419 (Mi izv1451)

Regular elements in spaces of linear representations of reductive algebraic groups

D. I. Panyushev

Abstract: A new proof is offered of a differential criterion of regularity for the adjoint representation of a semisimple connected group that does not use the existence of a section in the set of regular elements. Using the ideas of this proof, similar results are obtained for certain linear actions with a Cartan subspace, and, conversely, the existence of a section in the set of regular elements is proved.
Bibliography: 7 titles.

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English version:
Mathematics of the USSR-Izvestiya, 1985, 24:2, 383–390

Bibliographic databases:

UDC: 512
MSC: Primary 14L30, 20G05, 20G20; Secondary 17B10, 17B20

Citation: D. I. Panyushev, “Regular elements in spaces of linear representations of reductive algebraic groups”, Izv. Akad. Nauk SSSR Ser. Mat., 48:2 (1984), 411–419; Math. USSR-Izv., 24:2 (1985), 383–390

Citation in format AMSBIB
\Bibitem{Pan84} \by D.~I.~Panyushev \paper Regular elements in spaces of linear representations of reductive algebraic groups \jour Izv. Akad. Nauk SSSR Ser. Mat. \yr 1984 \vol 48 \issue 2 \pages 411--419 \mathnet{http://mi.mathnet.ru/izv1451} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=740797} \zmath{https://zbmath.org/?q=an:0557.20026} \transl \jour Math. USSR-Izv. \yr 1985 \vol 24 \issue 2 \pages 383--390 \crossref{https://doi.org/10.1070/IM1985v024n02ABEH001241} 

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This publication is cited in the following articles:
1. D. I. Panyushev, “Regular elements in spaces of linear representations. II”, Math. USSR-Izv., 27:2 (1986), 279–284
2. A. I. Bondal, “A symplectic groupoid of triangular bilinear forms and the braid group”, Izv. Math., 68:4 (2004), 659–708
3. Dmitri I. Panyushev, “On the coadjoint representation of -contractions of reductive Lie algebras”, Advances in Mathematics, 213:1 (2007), 380
4. Laudio Gorodski, “The discriminants associated to isotropy representations of symmetric spaces”, Transformation Groups, 2011
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