Even Partitions in Plethysms
arXiv:1003.4474 · doi:10.1016/j.jalgebra.2010.10.031
Abstract
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.
9 pages