Relations between the 2 × 2 minors of a generic matrix

We prove the case t = 2 of a conjecture Bruns-Conca-Varbaro, describing minimal relations between x minors generic matrix. Interpreting these as polynomial functors, and applying transpose duality in work Sam-Snowden, this problem is equivalent to understanding satisfied by generalized permanents. Our proof follows combining Koszul homology calculations on side, with study subspace varieties permanents Kempf-Weyman technique (on both sides).