The space of $n\times m$ complex matrices can be regarded as an algebraic variety on which the group ${\mathrm{GL}<!--FUNCTION\; APPLICATION-->}_n\times {\mathrm{GL}<!--FUNCTION\; APPLICATION-->}_m$ acts. There is a rich interaction between geometry and representation theory in this example. In an important paper, de Concini, Eisenbud, and Procesi classified the equivariant ideals in the coordinate ring. More recently, we proved a noetherian result for families of equivariant modules as $n$ and $m$ vary. We establish analogs of these results for the space of $(n|n)\times (m|m)$ isomeric matrices with respect to the action of $Q_n\times Q_m$, where $Q_n$ is the automorphism group of the isomeric structure (commonly known as the “queer supergroup”). Our work is motivated by connections to the Brauer category and the theory of twisted commutative algebras.

的空间$n\times 米$复矩阵可以看作是一个代数簇${\mathrm{总帐}<!--FUNCTION\; APPLICATION-->}_n\times {\mathrm{总帐}<!--FUNCTION\; APPLICATION-->}_{米}$行动。在这个例子中，几何和表示论之间存在着丰富的相互作用。在一篇重要论文中，de Concini、Eisenbud 和 Procesi 对坐标环中的等变理想进行了分类。最近，我们证明了等变模块族的诺特结果为$n$和$米$各不相同。我们为空间建立这些结果的类似物$(n|n)\times (米|米)$关于作用的异构矩阵${问}_n\times {问}_{米}$， 在哪里${问}_n$是异构结构的自同构群（俗称“酷儿超群”）。我们的工作受到与 Brauer 范畴和扭曲交换代数理论的联系的启发。