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The fundamental theorems of vector invariants. (English) Zbl 0668.15016

The author gives new proofs of the first fundamental theorems of vector invariants for special linear and special orthogonal groups. These proofs rely on reducing the theorems to the case of \(2\times 2\)-matrices; a close connection between the vector invariants of the special linear group or the special orthogonal group of \(n\times n\)-matrices, for all \(n\geq 2\), and those of the analogous group of \(2\times 2\)-matrices is used. This connection is described using the notion of leading monomials. Properties of leading monomials are also used to give new proofs of the second fundamental theorems of vector invariants for the geneal linear and orthogonal groups.
Reviewer: V.L.Popov

MSC:

15A72 Vector and tensor algebra, theory of invariants
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