Orbits of maximal dimension of solvable subgroups of reductive linear groups, and reduction for $U$-invariants

The article consists of three sections. In § 1, relations among the stationary subgroups are proved, and a method of computing $B_*$ from the structure of the algebra of covariants $k[V]^U$ is presented. § 2 contains a proof of a reduction theorem for covariants. In § 3, some examples are collected and some consideration given to the connection between the algebra of covariants $k[V]^U$ and the algebra of invariants $k[V\times V^*]^G$.
Bibliography: 15 titles.