Geometry of regular semisimple Lusztig varieties
演讲者
Jaehyun Hong
时间
2025年10月16日 15:00 至 16:00
地点
A6-101
线上
Zoom 262 865 5007
(YMSC)
摘要
In a series of papers, Lusztig developed a theory of characters of a reductive algebraic group G by using perverse sheaves on G. To get appropriate perverse sheaves on G (called character sheaves), he considered a family of subvarieties of the flag variety G/B parameterized by elements in G; now, we call Lusztig varieties. In this talk, we will explain how they are related to two interesting families of subvarieties of the flag variety, Schubert varieties and Hessenberg varieties. Regular semisimple Lusztig varieties share many nice properties with Schubert varieties. They are normal Cohen-Macaulay, have rational singularities, and are of Fano type. We construct a flat degeneration of regular semisimple Lusztig varieties to regular semisimple Hessenberg varieties and compare their cohomology spaces. This is joint work with P. Brosnan and D. Lee.