Even Partitions in Plethysms

Details Even Partitions in Plethysms Even Partitions in Plethysms

2010-03-23

arxiv.org/abs/1003.4474v2

Journal of Algebra 328, 322-329 (2011)

Mathematics

Group Theory

9 pages

Scientific paper

10.1016/j.jalgebra.2010.10.031

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.

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