Geodesic
Orbits of maximal dimension of~solvable subgroups of reductive linear groups, and reduction for $U$-invariants
Sbornik. Mathematics, Tome 60 (1988) no. 2, pp. 365-375

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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. 
@article{SM_1988_60_2_a6,
     author = {D. I. Panyushev},
     title = {Orbits of maximal dimension of~solvable subgroups of reductive linear groups, and reduction for $U$-invariants},
     journal = {Sbornik. Mathematics},
     pages = {365--375},
     publisher = {mathdoc},
     volume = {60},
     number = {2},
     year = {1988},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1988_60_2_a6/}
}
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D. I. Panyushev. Orbits of maximal dimension of~solvable subgroups of reductive linear groups, and reduction for $U$-invariants. Sbornik. Mathematics, Tome 60 (1988) no. 2, pp. 365-375. http://geodesic.mathdoc.fr/item/SM_1988_60_2_a6/