表示论研讨班：Good position braids, transversal slices and applications

中科院数学与系统科学研究院

数学研究所

学术报告

表示论研讨班

报告人：段承泽 博士（University of Maryland）   

题  目：Good position braids, transversal slices and applications

时  间：2023.12.20（星期三）10:00-11:00

地  点：zoom：89123111909 密码：20231220

摘  要：Let G be a reductive group over an algebraically closed field and W be its Weyl group. Using Coxeter elements, Steinberg constructed cross-sections of the adjoint quotient of G which also yield transversal slices of regular unipotent classes. In 2012, He and Lusztig constructed transversal slices using minimal length elements in elliptic conjugacy classes in W, which yield transversal slices of basic unipotent classes. In this talk, we generalize minimal length elements to good position braids in the associated braid monoid of W and use these elements to construct transversal slices of all unipotent classes in G. We shall see these new elements also appear in many other aspects of representation theory, such as affine Springer fibers and the partial order on unipotent classes, etc.