Equidimensional relatively stable reductive algebraic groups with simple commutator subgroups
The main result is the following theorem: Let \(G\) be a connected reductive algebraic group over \(\mathbb{C}\) whose commutator subgroup \(G'\) is a simple algebraic group. Let \(V\) be a finite-dimensional algebraic \(G\)-module. Assume that \(V\) is equidimensional and that there is a \(G\)-submodule \(U\) of \(V\) such that the natural action of \(G\) on \(U/ /G\) is stable and the inclusion \(U\hookrightarrow V\) induces an isomorphism \(U/ /G\simeq V/ /G\). Then \(V\) is cofree. -- This result is an indirect consequence of some explicit classifications obtained in this paper combined with further calculations and the known classifications.
scientific article; zbMATH DE number 1160717