@article{BIH-Permanent-Versus-Determinant-Not-Via-Saturations,
Title = {{Permanent Versus Determinant: Not Via Saturations}},
Author = {Peter Bürgisser and Christian Ikenmeyer and Jesko Hüttenhain},
Pages = {1247-1258},
Year = {2016},
Doi = {10.1090/proc/13310},
Journal = {Proc. AMS},
Volume = {145},
Month = {11},
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 $S(Det_n)$.},
Url = {http://arxiv.org/abs/1501.05528},
Url2 = {http://www3.math.tu-berlin.de/algebra/work/gct-sat-det-1.pdf}
}