Hyperpfaffians and Geometric Complexity Theory
Computational Complexity
2020-02-26 v2 Rings and Algebras
Representation Theory
Abstract
The hyperpfaffian polynomial was introduced by Barvinok in 1995 as a natural generalization of the well-known Pfaffian polynomial to higher order tensors. We prove that the hyperpfaffian is the unique smallest degree SL-invariant on the space of higher order tensors. We then study the hyperpfaffian's computational complexity and prove that it is VNP-complete. This disproves a conjecture of Mulmuley in geometric complexity theory about the computational complexity of invariant rings.
Cite
@article{arxiv.1912.09389,
title = {Hyperpfaffians and Geometric Complexity Theory},
author = {Christian Ikenmeyer and Michael Walter},
journal= {arXiv preprint arXiv:1912.09389},
year = {2020}
}
Comments
4 pages; results merged into arXiv:1910.01251