Коллоквиум ФКН "Bruhat interval polytopes which are cubes"

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Date: 18 мая, вторник, 16:20 – 17:40

Speaker: Mikiya Masuda, Osaka City University Advanced Mathematical Institute, HSE University

Topic: Bruhat interval polytopes which are cubes

Abstract

For a pair of permutations with in the Bruhat order, the Bruhat interval polytope is defined as the convex hull of points associated with permutations for . It lies in a permutohedron and is an example of a Coxeter matroid polytope.

The Bruhat interval polytope is the moment polytope of some subvariety of a flag variety called a Richardson variety and it is known that the Richardson variety is a smooth toric variety if and only if is combinatorially equivalent to a cube.

In this talk, I will explain that a certain family of Bruhat interval polytopes, which are particularly combinatorially equivalent to a cube, determines triangulations of a polygon. It turns out that the Wedderburn-Etherington numbers which count \emph{unordered} binary trees appear in their classification. If time permits, I will discuss another family of Bruhat interval polytopes and their classification, where directed paths, more generally directed Dynkin diagrams appear.

This talk is based on recent joint work with Eunjeong Lee (IBS-CGP) and Seonjeong Park (Jeonju Univ.).