The rationality of the fields of invariants of reducible representations of the group \(SL_ 2\)
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.
scientific article; zbMATH DE number 3931264