  We prove that for all natural numbers k,n,d with k <= d and every partition
lambda of size kn with at most k parts there exists an irreducible GL(d,
C)-representation of highest weight 2*lambda in the plethysm Sym^k(Sym^(2n)
(C^d)). This gives an affirmative answer to a conjecture by Weintraub (J.
Algebra, 129 (1):103-114, 1990). Our investigation is motivated by questions of
geometric complexity theory and uses ideas from quantum information theory.
