Seminar| Institute of Mathematical Sciences
Time：Friday, Apirl 21st, 2023, 10:00-11:00
Location：RS408, IMS
Speaker: Sian Nie, Academy of Mathematics and Systems Science, Chinese Academy of Sciences （聂思安，中科院数学与系统科学研究院）
Abstract: Let G be a simply connected semisimple group of rank r over an algebraically closed field. Steinberg has associated to each minimal length Coxeter element an r-dimensional affine space in G, which is a cross-section of all regular conjugacy classes of G. In this talk, we will consider natural analogues of Steinberg’s cross-sections in the context of a loop group equipped with a Frobenius automorphism. We will show how Steinberg’s cross-sections intersect Frobenius twisted conjugacy classes (which are parameterized by Newton polygons). Some interesting applications will also be discussed.