  Let $G$ be a complex reductive algebraic group, $g$ its Lie algebra and $h$ a
reductive subalgebra of $g$, $n$ a positive integer. Consider the diagonal
actions $G:g^n, N_G(h):h^n$. We study a relation between the algebra
$C[h^n]^{N_G(h)}$ and its subalgebra consisting of restrictions to $h^n$ of
elements of $C[g^n]^G$.

Representation Theory;Algebraic Geometry