No occurrence obstructions in geometric complexity theory

by Peter Burgisser, Christian Ikenmeyer, and Greta Panova

Oded's comments

Of course, I cannot really read this paper, but the result as stated in this paper sounds very interesting to me, albeit these are bad news (in some sense).

The original 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 (SIAM J Comput, 2008) 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.

See orignal report.

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