中科院数学与系统科学研究院

数学研究所

表示论研讨班

 

报告人何旭华 教授(香港中文大学)

 Affine Deligne-Lusztig varieties and Generalized affine Springer fibers

  2020.11.16(星期一),10:30-11:30

  点:数学院南楼N202

  要:The notion of affine Springer fiber was introduced by Kazhdan and Lusztig in 1988. It plays a crucial role in the geometric representation theory and the Langlands program. The generalized affine Springer fibers were first studied by Kottwitz and Viehmann for the hyperspecial level structure in 2012 and by Lusztig for arbitrary parahoric level structure in 2015. Many geometric properties for the hyperspecial level strucutre were further studied by Bouthier and Chi. In this talk, I will propose a new approach to study the generalized affine Springer fibers. The key observation is that the affine Deligne-Lusztig varieties, in some sense, may be regarded as the ``shadow'' of generalized affine Springer fibers. I will also explain some ingredients used to deduce some geometric properties (nonemptiness, dimension, irreducible components) of generalized affine Springer fibers from the properties of the affine Deligne-Lusztig varieties. This talk is based on a work in progress.

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