  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.
