Even partitions in plethysms

JOURNAL OF ALGEBRA

卷:328

Article

Buergisser, Peter²  Christandl, Matthias¹  Ikenmeyer, Christian² 

[1] Swiss Fed Inst Technol, Inst Theoret Phys, CH-8093 Zurich, Switzerland

[2] Univ Paderborn, Inst Math, D-33098 Paderborn, Germany

关键词: Group representation theory;    Plethysms;    Geometric complexity theory;    Quantum information theory;   

DOI  :  10.1016/j.jalgebra.2010.10.031

来源: Elsevier

【 摘 要 】

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 [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. (C) 2010 Elsevier Inc. All rights reserved.

【 授权许可】

Free