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

中文翻译：

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通用矩阵的 2 × 2 次要矩阵之间的关系

我们证明情况 $吨=2$ Bruns-Conca-Varbaro 的猜想，描述了 $吨\times 吨$通用矩阵的次要。将这些关系解释为多项式函子，并应用 Sam-Snowden 的工作中的转置对偶，这个问题相当于理解满足以下条件的关系$吨\times 吨$广义的永久物。我们的证明是通过将未成年人方面的 Koszul 同源性计算与永久方面的子空间变体研究以及 Kempf-Weyman 技术（双方）相结合来证明的。