Rectangular Kronecker Coefficients and Plethysms in Geometric Complexity Theory

Abstract

The geometric complexity theory program is an approach to separate algebraic complexity classes, more precisely to show the superpolynomial growth of the determinantal complexity dc(perm) of the permanent polynomial. Mulmuley and Sohoni showed that the vanishing behaviour of rectangular Kronecker coefficients could in principle be used to show some lower bounds on dc(perm) and they conjectured that superpolynomial lower bounds on dc(perm) could be shown in this way. In this paper we disprove this conjecture by Mulmuley and Sohoni, i.e., we prove that the vanishing of rectangular Kronecker coefficients cannot be used to prove superpolynomial lower bounds on dc(perm).