中国科学院数学与系统科学研究院

数学研究所

数学科学全国重点实验室

学术报告

表示论研讨班

Speaker: 桂弢博士（BICMR）

Inviter: 聂思安 研究员

Language: Chinese

Title: Peterson variety and total positivity

Time&Venue: 2025年6月26日（星期四） 14: 30-15: 30 & N818

Abstract:The Peterson variety is a remarkable subvariety of the flag variety, introduced by Dale Peterson to describe the quantum cohomology rings of all the (Langlands dual) partial flag varieties. On the other hand, many varieties that are important in Lie theory carry natural Lusztig positive structures. Of particular interests are the so-called regularity theorems on the totally nonnegative parts. By using toric geometry and the geometric Satake equivalence, we prove a folklore conjecture that the totally nonnegative part of the Peterson variety is a regular CW-complex which is homeomorphic to a cube as a cell decomposed space. This extend a theorem of Abe--Zeng (conjectured by Rietsch) in Lie type A to arbitrary Lie types. Based on joint work with Hiraku Abe and Haozhi Zeng.