0910.4512 (Peter Bürgisser et al.)

Nonvanishing of Kronecker coefficients for rectangular shapes    [PDF]

Peter Bürgisser, Matthias Christandl, Christian Ikenmeyer

We prove that for any partition $(\lambda_1,...,\lambda_{d^2})$ 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 $(k\lambda_1,...,k\lambda_{d^2})$. 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.

View original: http://arxiv.org/abs/0910.4512