—The permanent versus determinant conjecture is a major problem in complexity theory that is equivalent to the separation of the complexity classes VPws and VNP. Mulmuley and Sohoni [32] 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 approach to the permanent versus determinant problem via multiplicity obstructions as proposed in [32].

中文翻译：

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几何复杂性理论中无发生障碍

——永久对行列式猜想是复杂性理论中的一个主要问题，相当于复杂性类VPws和VNP的分离。Mulmuley 和 Sohoni [32] 建议在复数上研究这个猜想的强化版本，这相当于分离行列式和填充永久多项式的轨道闭合。在那篇论文中，还建议通过展示发生障碍来分离这些轨道闭合，这是 GL n 2 (C) 的不可约表示，出现在轨道闭合的一个坐标环中，但不在另一个坐标环中。我们证明这种方法是不可能的。然而，我们不排除通过 [32] 中提出的多重障碍解决永久与行列式问题的方法。