标题： 旗超流形的上同调和行列式理想的小化。 II 显示英文标题

标题： Cohomology of flag supervarieties and resolutions of determinantal ideals. II

摘要： 我们计算复数奇偶正则Grassmannian的结构层的相干上同调。 特别是，我们证明它可以分解为辛或正交群的Grassmannian的奇异上同调环与奇偶正则李超群的半单表示的张量积。 后者在其偶子群上的限制可以用Schur函子明确描述，并且与(skew-)对称行列式理想的关系密切。 我们开发了用于研究类型BC和D的Coxeter群的分裂环的工具，这可能具有独立的兴趣。 显示英文摘要

摘要： We compute the coherent cohomology of the structure sheaf of complex periplectic Grassmannians. In particular, we show that it can be decomposed as a tensor product of the singular cohomology ring of a Grassmannian for either the symplectic or orthogonal group together with a semisimple representation of the periplectic Lie supergroup. The restriction of the latter to its even subgroup has an explicit multiplicity-free description in terms of Schur functors and is closely related to syzygies of (skew-)symmetric determinantal ideals. We develop tools for studying splitting rings for Coxeter groups of types BC and D, which may be of independent interest.