Braid groups of type ADE, Garside monoids, and the categorified root lattice

Anthony M. Licata, Hoel Queffelec

We study Artin-Tits braid groups ${\mathbb{B}}_W$ of type ADE via the action of ${\mathbb{B}}_W$ on the homotopy category $\mathcal{K}$ of graded projective zigzag modules (which categ…