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Zbl 0817.22008
Aslaksen, Helmer; Tan, Eng-Chye; Zhu, Chen-Bo
Quivers and the invariant theory of Levi subgroups. (English)
[J] J. Funct. Anal. 120, No.1, 163-187 (1994). ISSN 0022-1236

We develop a theory of invariants using the formalism of quivers generalizing earlier results attributed to Procesi. This enables us to describe the invariant theory of certain block diagonal subgroups, generalizing results of Klink and Ton-That. As another application, let $H$ be the Levi component of a parabolic subgroup of a classical Lie group $G$ with Lie algebra $\germ g$. We describe a finite set of generators of ${\cal P}[{\germ g}]\sp H$, the space of $H$-invariant polynomials on ${\germ g}$, as well as the $H$-invariants in the universal enveloping algebra, ${\cal U}({\germ g})\sp H$, thus generalizing results of Klink and Ton-That, and Zhu.
[H.Aslaksen (Singapore)]

MSC 2000:: *22E45 Analytic repres.of Lie and linear algebraic groups over real fields
17B30 Solvable, nilpotent Lie algebras
15A72 Vector and tensor algebra
14L30 Group actions on varieties or schemes
22E60 Lie algebras of Lie groups

Keywords: theory of invariants; quivers; block diagonal subgroups; Levi component; parabolic subgroup; classical Lie group; Lie algebra; generators; universal enveloping algebra

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