Geodesic
Regular elements in spaces of linear representations of reductive algebraic groups
Izvestiya. Mathematics , Tome 24 (1985) no. 2, pp. 383-390

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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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     author = {D. I. Panyushev},
     title = {Regular elements in spaces of linear representations of reductive algebraic groups},
     journal = {Izvestiya. Mathematics },
     pages = {383--390},
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     year = {1985},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1985_24_2_a7/}
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D. I. Panyushev. Regular elements in spaces of linear representations of reductive algebraic groups. Izvestiya. Mathematics , Tome 24 (1985) no. 2, pp. 383-390. http://geodesic.mathdoc.fr/item/IM2_1985_24_2_a7/