Tan, Lin On the Popov-Pommerening conjecture for groups of type \(A_ n\). (English) Zbl 0682.14005 Proc. Am. Math. Soc. 106, No. 3, 611-616 (1989). The Popov-Pommerening conjecture claims that, given a reductive algebraic group G over an algebraically closed field k and a closed subgroup H of G which is normalized by a maximal torus of G, then for any affine algebraic G-variety X the algebra \(k[X]^ H\) of H-invariant regular functions on X is finitely generated. It is proved in the paper under review that the Popov-Pommerening conjecture is true if G is a reductive group of type \(A_ n\), \(n\leq 4\). It is also shown that there exists a Grosshans subgroup H of \(GL_ 5(k)\) such that the invariant subalgebra \(A^ H\) (where A is a “letter place algebra”) is not spanned by the invariant standard bitableaux. Reviewer: V.L.Popov Cited in 2 Documents MSC: 14L24 Geometric invariant theory 14L30 Group actions on varieties or schemes (quotients) 14L35 Classical groups (algebro-geometric aspects) 15A72 Vector and tensor algebra, theory of invariants Keywords:invariant regular functions; Popov-Pommerening conjecture; Grosshans subgroup; invariant standard bitableaux PDFBibTeX XMLCite \textit{L. Tan}, Proc. Am. Math. Soc. 106, No. 3, 611--616 (1989; Zbl 0682.14005) Full Text: DOI