MIT-Harvard-MSR COMBINATORICS SEMINAR

Friday, November 19, 2021 at 3:30pm to 4:30pm

Harvard University / 10 Oxford Street / Harvard Science Center 507 / Cambridge, MA

Speaker:  Grant Barkley  (Harvard University)

Title:  Extended weak order in affine type

Abstract

The extended weak order is a partial order associated to a Coxeter system (W, S). It is the containment order on ”biclosed” sets of positive roots in the (real) root system associated to W. When W is finite, this order coincides with the (right) weak order on W, but when W is infinite, the weak order on W is a proper order ideal in the extended weak order. It is well-known that the weak order on W is a lattice if and only if W is finite. In contrast, it is a longstanding conjecture of Matthew Dyer that the extended weak order is a lattice for any W, which is open in the case that W is infinite. I will present joint work with David Speyer where we prove this conjecture for the affine Coxeter groups.

Event Type

Conferences/Seminars/Lectures

Events By Interest

Academic

Events By Audience

Public

Website

https://math.mit.edu/sites/combin/

Department
Department of Mathematics
Contact Email

daisymae@math.mit.edu

Add to my calendar

Recent Activity