On the top-heaviness and unimodality of Bruhat intervals
发布时间：2023年09月30日
浏览次数：1947
发布者: Fei Tao
主讲人： Gaston Burrull(BICMR)
活动时间： 从 2023-10-09 15:00 到 16:30
场地： 北京国际数学研究中心，全斋全9教室
Abstract: This talk is about a concrete convex geometry problem related to the combinatorics of affine Schubert varieties X(w). I will introduce some basic notions with pictures and examples. I will introduce the notions of unimodality and top-heaviness for arbitrary sequences. Then I will explore these notions for the sequences biw of Betti numbers corresponding to the varieties X(w).
These sequences are always top-heavy, but not always unimodal. In the case of dominant elements in the affine Weyl group, the behavior of the corresponding sequences biw is described by a convex polyhedron that only depends on a dominant weight and the Cartan matrix of the corresponding (finite) root system. I will measure how top-heavy some of these sequences are, and state some results and conjectures. Examples in ranks 2, 3, and higher will be given.
These sequences are always top-heavy, but not always unimodal. In the case of dominant elements in the affine Weyl group, the behavior of the corresponding sequences biw is described by a convex polyhedron that only depends on a dominant weight and the Cartan matrix of the corresponding (finite) root system. I will measure how top-heavy some of these sequences are, and state some results and conjectures. Examples in ranks 2, 3, and higher will be given.
