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No occurence obstructions in geometric complexity theory
Citation key BIP - JAMS - No-Occurence-Obstructions-In-Geometric-Complexity-Theory
Author Peter Bürgisser and Christian Ikenmeyer and Greta Panova
Pages 163–193
Year 2019
DOI 10.1090/jams/908
Journal Journal of the American Mathematical Society
Volume 32
Number 1
Month 01
Abstract The permanent versus determinant conjecture is a major problem in complexity theory that is equivalent to the separation of the complexity classes $VP_ws$ and $VNP$. Mulmuley and Sohoni [37] suggested to study a strengthened version of this conjecture over the complex numbers that amounts to separating the orbit closures of the determinant and padded permanent polynomials. In that paper it was also proposed to separate these orbit closures by exhibiting occurrence obstructions, which are irreducible representations of $GL(n^2, C)$, which occur in one coordinate ring of the orbit closure, but not in the other. We prove that this approach is impossible. However, we do not rule out the general approach to the permanent versus determinant problem via multiplicity obstructions as proposed in [37].
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