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The rationality of the fields of invariants of reducible representations of the group \(SL_ 2\). (English. Russian original) Zbl 0582.20032
Mosc. Univ. Math. Bull. 39, No. 5, 80-83 (1984); translation from Vestn. Mosk. Univ., Ser. I 1984, No. 5, 77-79 (1984).
Let V(d) be the space of homogeneous polynomials of degree d in two variables, and \(V=V(d(1))\times...\times V(d(k))\) for some d(1),...,d(k). On V there exists a natural action of the group \(G=SL_ 2\times ({\mathbb{C}}^*)^ k\). The main theorem of the note states that the field of invariants \({\mathbb{C}}[V]^ G\) is rational for all k with the only possible exception \(k=1\), d(1) even.
Reviewer: S.I.Gel’fand

20G05 Representation theory for linear algebraic groups
15A72 Vector and tensor algebra, theory of invariants