Geodesic
Invariants of the adjoint action on nil-radicals of parabolic subalgebras in $B_n$, $C_n$, $D_n$
Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 20, Tome 386 (2011), pp. 265-280 
V. V. Sevostianova. Invariants of the adjoint action on nil-radicals of parabolic subalgebras in $B_n$, $C_n$, $D_n$. Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 20, Tome 386 (2011), pp. 265-280. http://geodesic.mathdoc.fr/item/ZNSL_2011_386_a7/
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     title = {Invariants of the adjoint action on nil-radicals of parabolic subalgebras in $B_n$, $C_n$, $D_n$},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {265--280},
     year = {2011},
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     url = {http://geodesic.mathdoc.fr/item/ZNSL_2011_386_a7/}
}
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Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

We consider the conjugation action of the unitriangular subgroup $N$ of one of the following groups $\mathrm{Sp}_{2n}$, $\mathrm O_{2n}$, $\mathrm O_{2n+1}$, on the nilradical of a parabolic subalgebra in the corresponding Lie algebra. We introduce the notion of an extended base in the set of positive roots. To each root of the extended base there corresponds an invariant with respect to the adjoint action of $N$. We show that these invariants are algebraically independent. Also, we estimate trancendence degrees of these invariants. Bibl. 6 titles.

[1] E. B. Vinberg, V. L. Popov, “Teoriya invariantov”, Itogi nauki i tekhniki. Sovr. prob. matematiki. Fund. napravl., 55, VINITI, M., 1989, 137—309 | MR | Zbl

[2] M. Goto, F. Grosskhans, Poluprostye algebry Li, Mir, M., 1981 | MR | Zbl

[3] Kh. Kraft, Geometricheskie metody v teorii invariantov, Mir, M., 1987 | MR | Zbl

[4] A. N. Panov, V. V. Sevostyanova, “Regulyarnye $N$-orbity v nilradikale parabolicheskoi podalgebry”, Tr. mezhd. konf. po algebre i teorii chisel, posv. 80-letiyu V. E. Voskresenskogo, Izd. “Samarskii universitet”, 2007, 152–161

[5] V. V. Sevostyanova, “Pole invariantov prisoedinënnogo deistviya unitreugolnoi gruppy v nilradikale parabolicheskoi podalgebry”, Zap. nauchn. semin. POMI, 375, 2010, 167–194 | MR | Zbl

[6] V. V. Sevostyanova, “Algebra invariantov prisoedinënnogo deistviya unitreugolnoi gruppy v nilradikale parabolicheskoi podalgebry”, Vestnik SamGU, Estestvennonauchnaya seriya, 2010, no. 2(76), 72–83