This article is cited in 4 scientific papers (total in 4 papers)
A finiteness theorem for representations with a free algebra of invariants
V. L. Popov
It is proved that for any connected semisimple algebraic group $G$ defined over an algebraically closed field of characteristic zero there exist (up to isomorphism) only a finite number of finite-dimensional rational $G$-modules containing no nonzero fixed vectors and having a free algebra of invariants. The proof is constructive and makes it possible in principle to indicate these $G$-modules explicitly. It is also proved that for all irreducible $G$-modules $V$, except for a finite number, the degree of the Poincaré series of the algebra of invariants (regarded as a rational function) equals $-\dim V$.
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Mathematics of the USSR-Izvestiya, 1983, 20:2, 333–354
MSC: Primary 15A72, 20G05; Secondary 52A25
V. L. Popov, “A finiteness theorem for representations with a free algebra of invariants”, Izv. Akad. Nauk SSSR Ser. Mat., 46:2 (1982), 347–370; Math. USSR-Izv., 20:2 (1983), 333–354
Citation in format AMSBIB
\paper A~finiteness theorem for representations with a~free algebra of invariants
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\jour Math. USSR-Izv.
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This publication is cited in the following articles:
V. L. Popov, “Syzygies in the theory of invariants”, Math. USSR-Izv., 22:3 (1984), 507–585
D. I. Panyushev, “Regular elements in spaces of linear representations of reductive algebraic groups”, Math. USSR-Izv., 24:2 (1985), 383–390
N Alon, K.A Berman, “Regular hypergraphs, Gordon's lemma, Steinitz' lemma and invariant theory”, Journal of Combinatorial Theory, Series A, 43:1 (1986), 91
D. I. Panyushev, “Orbits of maximal dimension of solvable subgroups of reductive linear groups, and reduction for $U$-invariants”, Math. USSR-Sb., 60:2 (1988), 365–375
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