Speaker: 桂弢博士，BICMR

Inviter: 聂思安研究员

Title: Peterson variety and total positivity

Language: Chinese

Time & Venue: 2025.06.26 14:30-15:30 南楼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.