First Fundamental Theorem of Invariant Theory for covariants of classical groups

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.