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Even partitions in plethysms
Citation key BCI-Even-Partitions-In-Plethysms
Author Peter Bürgisser and Matthias Christandl and Christian Ikenmeyer
Pages 322-329
Year 2011
Journal Journal of Algebra
Volume 328
Abstract We prove that for all natural numbers $k,n,d$ with $kłe d$ and every partition λ of size $kn$ with at most $k$ parts there exists an irreducible $\mathrmGL(d,\mathbb C)$-representation of highest weight $2\cdotłambda$ in the plethysm $\mathrmSym^k \mathrmSym^2n (C^d)$. 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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