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.
\Bibitem{Pan84}
\by D.~I.~Panyushev
\paper Regular elements in spaces of linear representations of reductive algebraic groups
\jour Math. USSR-Izv.
\yr 1985
\vol 24
\issue 2
\pages 383--390
\mathnet{http://mi.mathnet.ru/eng/im1451}
\crossref{https://doi.org/10.1070/IM1985v024n02ABEH001241}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=740797}
\zmath{https://zbmath.org/?q=an:0557.20026}
Citation in format AMSBIB
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