Combinatorial Theory

For affine Coxeter groups of affine types \(\widetilde{\text{D}}\) and \(\widetilde{\text{B}}\), we model the interval \([1,c]_T\) in the absolute order by symmetric noncrossing partitions of an annulus with one or two double points. In type \(\widetilde{\text{B}}\) (and almost in type \(\widetilde{\text{D}}\)), the diagrams also model the larger lattice defined by McCammond and Sulway.

Mathematics Subject Classifications: Primary: 20F55, 05E16; Secondary: 20F36

Keywords: Absolute order, affine Coxeter group, marked surface, noncrossing partition