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Nonvanishing of Kronecker coefficients for rectangular shapes
Citation key BCI-Nonvanishing-Of-Kronecker-Coefficients-For-Rectangular-Shapes
Author Peter Bürgisser and Matthias Christandl and Christian Ikenmeyer
Pages 2082-2091
Year 2011
Journal Advances in Mathematics
Volume 227
Abstract We prove that for any partition $(łambda_1,...,łambda_d^2)$ of size $\ell d$ there exists $k\ge 1$ such that the tensor square of the irreducible representation of the symmetric group $S_k\ell d$ with respect to the rectangular partition $(k\ell,...,k\ell)$ contains the irreducible representation corresponding to the stretched partition $(kłambda_1,...,kłambda_d^2)$. We also prove a related approximate version of this statement in which the stretching factor $k$ is effectively bounded in terms of $d$. This investigation is motivated by questions of geometric complexity theory.
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