Article ID Journal Published Year Pages File Type
4586496 Journal of Algebra 2011 8 Pages PDF
Abstract

We prove that for all natural numbers k,n,d with k⩽d and every partition λ of size kn with at most k parts there exists an irreducible GLd(C)-representation of highest weight 2λ in the plethysm Symk(Sym2nCd). This gives an affirmative answer to a conjecture by Weintraub [Steven H. Weintraub, Some observations on plethysms, J. Algebra 129 (1) (1990) 103–114]. Our investigation is motivated by questions of geometric complexity theory and uses ideas from quantum information theory.

Related Topics
Physical Sciences and Engineering Mathematics Algebra and Number Theory