论文标题
迈向彼得森品种和理查森品种的交叉点
Toward cohomology rings of intersections of Peterson varieties and Richardson varieties
论文作者
论文摘要
彼得森的品种是旗品的亚变化，其（等效性的）共同体学是由福川川 - 哈拉达·马苏达（Fukukawa-Harada-Masuda）在A型中给出的，随后不久，随后的作者和Masuda的作者明确地呈现了（Equivariant）的同类综合戒指，以供Peterson品种提供彼得森品种，以供彼得森（Peterson）品种用于自其谎言类型。在本说明中，我们研究了Peterson品种与Schubert，Schubert对面和Richardson品种的（彼得）共同体学环的（均等）的共同体学环。根据Goldin-Mihalcea-Singh的工作，彼得森品种与舒伯特品种的交集自然可以用较小的彼得森品种鉴定出来，因此问题减少了相反的舒伯特交叉点的问题。在本说明中，我们为（peterson品种条件的某些条件）提供了（epoiriant）的共同体学戒指的技术声明。通过使用该陈述，我们计算了彼得森品种的某些相互作用的（等效性的）共同体学。与A型相反的Schubert品种相反。我们还明确地呈现了彼得森品种与Richardson品种类型A的某些相互作用的（等效性的）共同体学环。
Peterson varieties are subvarieties of flag varieties and their (equivariant) cohomology rings are given by Fukukawa-Harada-Masuda in type A and soon later the author with Harada and Masuda gives an explicit presentation of the (equivariant) cohomology rings of Peterson varieties for arbitrary Lie types. In this note we study the (equivariant) cohomology ring of the intersections of Peterson variety with Schubert, opposite Schubert, and Richardson varieties in more general. By the work of Goldin-Mihalcea-Singh, the intersections of Peterson variety with Schubert varieties are naturally identified with smaller Peterson varieties, so the problem reduces to the problem for opposite Schubert intersections. In this note we provide a technical statement for (equivariant) cohomology ring of a subvariety with some conditions of Peterson variety. By using the statement, we calculate the (equivariant) cohomology rings for some intersections of Peterson varieties with opposite Schubert varieties in type A. We also explicitly present the (equivariant) cohomology rings for some intersections of Peterson varieties with Richardson varieties in type A.
