First Fundamental Theorem of Invariant Theory for covariants of classical groups

D. A. Shmel'kin

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First Fundamental Theorem of Invariant Theory for covariants of classical groups

D. A. Shmel'kin

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Abstract

Let $U(G)$ be a maximal unipotent subgroup of one of classical groups $G=GL(V),O(V),Sp(V)$. Let $W$ be a direct sum of copies of $V$ and its dual $V*$. For the natural action $U(G):W$, we describe a minimal system of homogeneous generators for the algebra of $U(G)$-invariant regular functions on $W$. For $G=GL(V)$, we also describe the syzygies among these generators in some particular cases.

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BibTeX RIS

D. A. Shmel'kin. 2000-06-15. First Fundamental Theorem of Invariant Theory for covariants of classical groups. https://arxiv.org/abs/math/0006110

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