Geodesic
The theorem on restriction of invariants, and nilpotent elements in $W_n$
Sbornik. Mathematics, Tome 73 (1992) no. 1, pp. 135-159 Cet article a éte moissonné depuis la source Math-Net.Ru

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The ring of invariant polynomial functions on the general algebra of Cartan type $W_n$ is described explicitly. It is assumed that the ground field is algebraically closed and its characteristic is greater than 2. This result is used to prove that the variety of nilpotent elements in $W_n$ is an irreducible complete intersection and contains an open orbit whose complement consists of singular points. Moreover, a criterion for orbits in $W_n$ to be closed is obtained, and it is proved that the action of the commutator subgroup of the automorphism group in $W_n$ is stable. 
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     title = {The theorem on restriction of invariants, and nilpotent elements in~$W_n$},
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     url = {http://geodesic.mathdoc.fr/item/SM_1992_73_1_a7/}
}
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A. A. Premet. The theorem on restriction of invariants, and nilpotent elements in $W_n$. Sbornik. Mathematics, Tome 73 (1992) no. 1, pp. 135-159. http://geodesic.mathdoc.fr/item/SM_1992_73_1_a7/

[1] Shafarevich I. R., Osnovy algebraicheskoi geometrii, Nauka, M., 1972 | MR | Zbl

[2] Khamfri Dzh., Lineinye algebraicheskie gruppy, Nauka, M., 1980 | MR

[3] Diksme Zh., Universalnye obertyvayuschie algebry, Mir, M., 1978 | MR

[4] Burbaki N., Gruppy i algebry Li, Glavy IV, V, VI, Mir, M., 1972 | MR | Zbl

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

[6] Rudakov A. N., “Gruppy avtomorfizmov beskonechnomernykh prostykh algebr Li”, Izv. AN SSSR. Ser. matem., 33:4 (1969), 748–764 | MR | Zbl

[7] Demushkin S. P., “Podalgebry Kartana prostykh $p$-algebr Li $W_n$ i $S_n$”, Sib. matem. zhurn., XI:2 (1970), 310–325

[8] Vinberg E. B., “Gruppa Veilya graduirovannoi algebry Li”, Izv. AN SSSR. Ser. matem., 40:3 (1976), 488–526 | MR | Zbl

[9] Popov V. L., “Zamknutye orbity borelevskikh podgrupp”, Matem. sb., 135(177) (1988), 385–402 | MR

[10] Dickson L. E., “A fundamental system of invariants of the general modular linear group with a solution of the form problem”, Trans. Amer. Math. Soc., 2 (1911), 75–98 | DOI | MR

[11] Kostant B., “Lie group representations on polynomial rings”, Amer. J. Math., 85:3 (1963), 327–404 | DOI | MR | Zbl

[12] Kostant B., Rallis S., “Orbits and representations associated with symmetric spaces”, Amer. J. Math., 93 (1971), 753–809 | DOI | MR | Zbl

[13] Kac V. G., Popov V. L., Vinberg E. B., “Sur les groupes lineaires algebriques dont l'algebre des invariants est libre”, C. R. Acad. Sci. Paris, 283 (1976), 875–878 | MR | Zbl

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

[15] Steinberg R., “Conjugacy classes in algebraic groups”, Lecture Notes Math., 366 (1974), 1–159 | DOI | MR

[16] Donkin S., “On conjugating representations and adjoint representations of semisimple groups”, Invent. Math., 91 (1988), 137–145 | DOI | MR | Zbl