Poset Structure Concerning Cylindric Diagrams

Abstract

Cylindric diagrams admit the structure of infinite $d$-complete posets with natural ordering. The purpose of this paper is to provide a realization of a cylindric diagram as a subset of an affine root system of type A via colored hook lengths and to present several characterizations of its poset structure. Furthermore, the set of order ideals of a cylindric diagram is described as a weak Bruhat interval of the affine Weyl group.