Permanent versus determinant: Not via saturations

作者: Peter Bürgisser , Christian Ikenmeyer , Jesko Hüttenhain

DOI: 10.1090/PROC/13310

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摘要: Let Det_n denote the closure of GL_{n^2}(C)-orbit determinant polynomial det_n with respect to linear substitution. The highest weights (partitions) irreducible GL_{n^2}(C)-representations occurring in coordinate ring form a finitely generated monoid S(Det_n). We prove that saturation S(Det_n) contains all partitions lambda length at most n and size divisible by n. This implies representation theoretic obstructions for permanent versus problem must be holes

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