Harvard-MIT-MSR Combinatorics Seminar


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November 19, 2021 3:30 pm - 4:30 pm
Science Center 507
Address: 1 Oxford Street, Cambridge, MA 02138 USA

Grant Barkley - Harvard University

will speak on:

Extended weak order in affine type

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.