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Hyperpfaffians and Geometric Complexity Theory

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arxiv 1912.09389 v2 pith:ED2QQEWH submitted 2019-12-19 cs.CC math.RAmath.RT

Christian Ikenmeyer , Michael Walter This is my paper · ORCID
classification cs.CCmath.RAmath.RT
keywords complexityhyperpfaffiancomputationalgeometrichigherorderpolynomialprove
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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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