Symmetric noncrossing partitions of an annulus with double points

Abstract

For affine Coxeter groups of affine types $\tilde{D}$ and $\tilde{B}$, 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 $\tilde{B}$ (and \emph{almost} in type $\tilde{D}$), the diagrams also model the larger lattice defined by McCammond and Sulway.

arXiv comment51 pages, 6 figures. Version 2: Small revisions and improvements throughout. Version 3: Small revisions and improvements, thanks to two anonymous referees. Version 4: final pre-publication version