Affine Dual Braid Monoids: Finite Cores, Exceptional Cluster Complexes, and Koszul Resolutions

Jindong Yan, Shenglin Zhu

For every finite-rank crystallographic affine Coxeter system $(W,S)$ and Coxeter element $c$, we construct a minimal linear graded free resolution of the trivial module over $k[M([…