中科院数学与系统科学研究院
数学研究所
表示论研讨班
报告人： 洪久族 教授（university of North Carolina at Chapel Hill）
题 目：A combinatorial study of affine Schubert varieties in affine Grassmannian
时 间：2019.07.05（星期五），16:00-17:00
地 点：数学院南楼N702室
摘 要：We study the combinatorial properties of affine Schubert varieties, the closure of the orbits of the Iwahori subgroup I in affine Grassmannian Gr of a simple algebraic group G of adjoint type. In this talk, I will explain a simple algorithm which describes all I-orbits in an affine Schubert variety in terms of coweights. I will explain the behavior of the closure relations of I-orbits in each chamber of the coweight lattice, and the behavior after crossing the walls of chambers. I will also explain a combinatorial duality between affine Schubert varieties in Gr and level one affine Demazure modules of the Kac-Moody algebra with the Dynkin diagram dual to the extended Dynkin diagram of G. This talk will be based on the joint work with Marc Besson.