Benson, Chal; Ratcliff, Gail A classification of multiplicity free actions. (English) Zbl 0869.14021 J. Algebra 181, No. 1, 152-186 (1996). This paper is concerned with the classification of multiplicity-free linear actions of reductive complex algebraic groups on vector spaces. The action of a complex reductive algebraic group \(G\) on an affine variety \(V\) is called multiplicity-free if each irreducible representation of \(G\) occurs at most once in the ring of regular functions \(C[V]\). A complete classification of multiplicity-free actions where \(V\) is an irreducible \(G\)-module was given by V. Kac [J. Algebra 64, 190-213 (1980; Zbl 0431.17007)]. In this article, the authors give a classification where \(V\) is a \(G\)-module, but not irreducible. They find many examples where the action does not decompose into a direct product of irreducible actions. Reviewer: L.Moser-Jauslin (Dijon) Cited in 4 ReviewsCited in 36 Documents MSC: 14L30 Group actions on varieties or schemes (quotients) Keywords:actions of reductive complex algebraic groups; multiplicity-free actions Citations:Zbl 0431.17007 PDFBibTeX XMLCite \textit{C. Benson} and \textit{G. Ratcliff}, J. Algebra 181, No. 1, 152--186 (1996; Zbl 0869.14021) Full Text: DOI