Topology of Hessenberg varieties and representations of symmetric groups

2017 Fiscal Year Final Research Report

• Project/Area Number: 15K17544
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Multi-year Fund
• Research Field: Geometry
• Research Institution: Osaka City University
• Principal Investigator: Abe Hiraku 大阪市立大学, 大学院理学研究科, 数学研究所専任研究所員 (00736499)
• Project Period (FY): 2015-04-01 – 2018-03-31
• Keywords: 旗多様体 / Hessenberg多様体 / トーリック多様体 / コホモロジー環 / 対称群の表現

Outline of Final Research Achievements

We studied the ring structures of the cohomology of Hessenberg varieties.
(1)We explicitly determined the cohomology ring of an arbitrary regular nilpotent Hessenberg variety in Lie type A, and we also proved that it is isomorphic (as rings) to the symmetric group invariant subring of the cohomology ring of the corresponding regular semisimple Hessenberg variety. (2)For a Hessenberg function of special form, we explicitly determined the cohomology ring of the regular semisimple Hessenberg variety in Lie type A. (3)We gave a certain presentation of the cohomology ring of an arbitrary Hessenberg variety for the minimal nilpotent orbit.

Free Research Field

代数多様体のトポロジー