Geodesic
A~finiteness theorem for representations with a~free algebra of invariants
Izvestiya. Mathematics , Tome 20 (1983) no. 2, pp. 333-354

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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 $-\dim V$. Bibliography: 21 titles. 
@article{IM2_1983_20_2_a6,
     author = {V. L. Popov},
     title = {A~finiteness theorem for representations with a~free algebra of invariants},
     journal = {Izvestiya. Mathematics },
     pages = {333--354},
     publisher = {mathdoc},
     volume = {20},
     number = {2},
     year = {1983},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1983_20_2_a6/}
}
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V. L. Popov. A~finiteness theorem for representations with a~free algebra of invariants. Izvestiya. Mathematics , Tome 20 (1983) no. 2, pp. 333-354. http://geodesic.mathdoc.fr/item/IM2_1983_20_2_a6/