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Invariants of sets of linear varieties. (English) Zbl 0717.15020

The author announces the computation of a minimal set of generators of the ring of invariants for four linear subspaces of dimension n in a vector space of dimension 2n. This computation is based on the symbolic method developed by F. D. Grosshans, G.-C. Rota and J. A. Stein [Invariant theory and superalgebras (1987; Zbl 0648.15020)]
A complete set of invariants for five 3-dimensional subspaces in a vector space of dimension 6 has also been determined. This result will be published later.
The problem of the determination of a complete set of invariants for four n-dimensional subspaces in a 2n-dimensional vector space is due to H. W. Turnbull [Proc. Edinburgh Math. Soc. (2)7, 55-72 (1942; Zbl 0063.07882)].
Reviewer: A.A.Premet

MSC:

15A72 Vector and tensor algebra, theory of invariants
65F30 Other matrix algorithms (MSC2010)
68W30 Symbolic computation and algebraic computation
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