@article{BIP - JAMS - No-Occurence-Obstructions-In-Geometric-Complexity-Theory,
Title = {No occurence obstructions in geometric complexity theory},
Author = {Peter B\"urgisser 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].},
Url = {https://arxiv.org/abs/1604.06431},
Url2 = {http://www.ams.org/journals/jams/2019-32-01/S0894-0347-2018-00908-7/S0894-0347-2018-00908-7.pdf}
}