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| Zitatschlüssel | BIH-Permanent-Versus-Determinant-Not-Via-Saturations |
|---|---|
| Autor | Peter Bürgisser and Christian Ikenmeyer and Jesko Hüttenhain |
| Seiten | 1247-1258 |
| Jahr | 2016 |
| DOI | 10.1090/proc/13310 |
| Journal | Proc. AMS |
| Jahrgang | 145 |
| Monat | 11 |
| Zusammenfassung | 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 λ 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 $S(Det_n)$. |