摘要： For an algebraic group $G$, Lusztig generalized the classical Springer correspondence to give a bijection between the set of $G$-equivariant perverse sheaves on the unipotent variety, and a union of irreducible representations of some Coxeter groups, including the Weyl group of $G$. The Springer map is a key ingredient of the Springer correspondence. The fibers of this map are called Springer fibers, which are a special kind of Spaltenstein varieties. Many structural properties of Spaltenstein varieties are revealed by Borho-MacPherson.
In this talk, we will consider the symmetric spaces associated to orthogonal groups, with the base field of odd characteristic. We will explain the generalized Springer correspondence in this case. Also, the Spaltenstein varieties will be considered, and an algorithm will be given for the calculation of Green functions in this case.
报告人简介：杨高博士，2016年毕业于华东师范大学，师从时俭益教授。获博士学位。2016年至今，在同济大学做博士后研究。合作导师为日本著名数学家Shoji教授。 杨高博士主要从事Lusztig胞腔理论与Springer理论研究。她自己独立，以及分别与时俭益教授，Shoji教授合作获得了多项重要的研究成果。