@UNPUBLISHED{BIH-Permanent-Versus-Determinant-Not-Via-Saturations,
 TITLE={Permanent versus determinant: not via saturations},
 URL={http://arxiv.org/abs/1501.05528},
 NOTE={To appear in Proc. AMS},
 AUTHOR={Peter Bürgisser and Christian Ikenmeyer and Jesko Hüttenhain},
 YEAR={2015},
 ABSTRACT={Let $Det_n$ denote the closure of the $\mathrm G\mathrm L(n^2,\mathbb C)$-orbit of the determinant polynomial $\det_n$ with respect to linear substitution. The highest weights (partitions) of irreducible $\mathrm G\mathrm L(n^2,\mathbb C)$-representations occurring in the coordinate ring of $Det_n$ form a finitely generated monoid $S(Det_n)$. We prove that the saturation of $S(Det_n)$ contains all partitions $\lambda$ with length at most $n$ and size divisible by $n$. This implies that representation theoretic obstructions for the permanent versus determinant problem must be holes of the monoid $S(Det_n)$.},
 MONTH={07}
}

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