Cambrian fans
For a finite Coxeter group and a Coxeter element of ; the -Cambrian fan is a coarsening of the fan defined by the reflecting hyperplanes of . Its maximal cones are naturally indexed by the -sortable elements of . The main result of this paper is that the known bijection cl between -sortable elements and -clusters induces a combinatorial isomorphism of fans. In particular, the -Cambrian fan is combinatorially isomorphic to the normal fan of the generalized associahedron for . The rays...