No occurrence obstructions in geometric complexity theory [article]

Peter Bürgisser and Christian Ikenmeyer and Greta Panova
2018 arXiv   pre-print
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., 2001) 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,
more » ... ich 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 by Mulmuley and Sohoni.
arXiv:1604.06431v3 fatcat:7bnkt3tyvjb6jaubwrmpvuuhsi