Hyperpfaffians and Geometric Complexity Theory

Christian Ikenmeyer; Michael Walter

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arXiv · 1912.09389

Hyperpfaffians and Geometric Complexity Theory

Christian Ikenmeyer·Michael Walter

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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.

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Christian Ikenmeyer, Michael Walter. 2019-12-19. Hyperpfaffians and Geometric Complexity Theory. https://arxiv.org/abs/1912.09389

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