Relative equidimensionality and stability of actions of a reductive algebraic group
The author introduces and studies relative versions of equidimensionality and stability, notions of algebraic transformation groups theory. They are called relative quasi-equidimensionality and relative stability of actions of affine algebraic groups, especially of reductive groups, on affine varieties. As an application, for complex reductive groups of semisimple rank one, the author characterizes relatively stable representations and relatively equidimensional representations, and shows that every equidimensional representation is cofree.
scientific article; zbMATH DE number 1491671