Abstract:
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.
\Bibitem{Pre91}
\by A.~A.~Premet
\paper The theorem on restriction of invariants, and nilpotent elements in~$W_n$
\jour Math. USSR-Sb.
\yr 1992
\vol 73
\issue 1
\pages 135--159
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\crossref{https://doi.org/10.1070/SM1992v073n01ABEH002538}
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This publication is cited in the following 19 articles:
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Ke Ou, Bin Shu, Yu Feng Yao, “On Chevalley Restriction Theorem for Semi-reductive Algebraic Groups and Its Applications”, Acta. Math. Sin.-English Ser., 38:8 (2022), 1421
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Hao Chang, “Adjoint quotient maps for the restricted Lie algebrasWnandSn”, Communications in Algebra, 45:1 (2017), 47
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Yu-Feng Yao, “On nilpotent commuting varieties of r-tuples in the Witt algebra”, Journal of Pure and Applied Algebra, 219:9 (2015), 4042
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Yu-Feng Yao, Hao Chang, “The nilpotent commuting variety of the Witt algebra”, Journal of Pure and Applied Algebra, 2014
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Hao Chang, Yu-Feng Yao, “On $${\mathbb{F}_q}$$ F q -Rational Structure of Nilpotent Orbits in the Witt Algebra”, Results. Math, 2013
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