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
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- The Spectra of Density Operators and the Kronecker Coefficients of the Symmetric Group
- Quantum marginal problem and representations of the symmetric group
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- An overview of mathematical issues arising in the Geometric complexity theory approach to VP v.s. VNP
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- Equations for secant varieties of Chow varieties
- Young Flattenings in the Schur module basis