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Description: |
The characteristic zero approach can be founded on the so-called Weyl's Theorem (H. Weyl, The Classical Groups, 1946) which essentially says that a system of generators for the algebra of (absolute) vector invariants for any subgroup G of GL(d) can be constructed by polarizing a system of generators of the invariants in d vector variables. We show that Weyl's Theorem can be regarded as an immediate corollary of a beautiful combinatorial identity, the Gordan-Capelli-Deruyts polar expansion formula. Then, we briefly discuss the way to derive from Weyl's Theorem the basic invariant theory for the groups SL(d), Sp2m, SO(d), O(d).
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