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Mat. Sb. (N.S.), 1987, Volume 132(174), Number 3, Pages 371–382 (Mi msb1870)  

This article is cited in 4 scientific papers (total in 4 papers)

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

D. I. Panyushev


Abstract: 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.

Full text: PDF file (750 kB)
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English version:
Mathematics of the USSR-Sbornik, 1988, 60:2, 365–375

Bibliographic databases:

UDC: 512
MSC: Primary 20G15; Secondary 14K05
Received: 11.10.1985 and 01.07.1986

Citation: D. I. Panyushev, “Orbits of maximal dimension of solvable subgroups of reductive linear groups, and reduction for $U$-invariants”, Mat. Sb. (N.S.), 132(174):3 (1987), 371–382; Math. USSR-Sb., 60:2 (1988), 365–375

Citation in format AMSBIB
\Bibitem{Pan87}
\by D.~I.~Panyushev
\paper Orbits of maximal dimension of~solvable subgroups of reductive linear groups, and reduction for $U$-invariants
\jour Mat. Sb. (N.S.)
\yr 1987
\vol 132(174)
\issue 3
\pages 371--382
\mathnet{http://mi.mathnet.ru/msb1870}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=889598}
\zmath{https://zbmath.org/?q=an:0663.20044|0628.20034}
\transl
\jour Math. USSR-Sb.
\yr 1988
\vol 60
\issue 2
\pages 365--375
\crossref{https://doi.org/10.1070/SM1988v060n02ABEH003174}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. V. L. Popov, “Closed orbits of Borel subgroups”, Math. USSR-Sb., 63:2 (1989), 375–392  mathnet  crossref  mathscinet  zmath
    2. Paniushev D., “Complexity and Rank of Uniform-Spaces and Coisotropy Representation”, 307, no. 2, 1989, 276–279  isi
    3. Panyushev D., “Complexity and Rank of Homogeneous Spaces”, Geod. Dedic., 34:3 (1990), 249–269  mathscinet  zmath  isi
    4. D. I. Panyushev, “Complexity and rank of double cones and tensor product decompositions”, Comment Math Helv, 68:1 (1993), 455  crossref  mathscinet  zmath  isi
  • Математический сборник (новая серия) - 1964–1988 Sbornik: Mathematics (from 1967)
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