@article{BCI-Even-Partitions-In-Plethysms,
Title = {Even partitions in plethysms},
Author = {Peter Bürgisser and Matthias Christandl and Christian Ikenmeyer},
Pages = {322-329},
Year = {2011},
Journal = {Journal of Algebra},
Volume = {328},
Abstract = {We prove that for all natural numbers $k,n,d$ with $k\le d$ and every partition $\lambda$ of size $kn$ with at most $k$ parts there exists an irreducible $\mathrm{GL}(d,\mathbb C)$-representation of highest weight $2\cdot\lambda$ in the plethysm $\mathrm{Sym}^k \mathrm{Sym}^{2n} (C^d)$. 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.},
Url = {http://arxiv.org/abs/1003.4474v1},
Url2 = {http://www3.math.tu-berlin.de/algebra/work/weintraub.pdf}
}