Poset Structure concerning Cylindric Diagrams

TL;DR

This paper explores the structure of cylindric diagrams by representing them within root systems of affine type A and characterizing their poset properties, linking order ideals to weak Bruhat intervals in Weyl groups.

Contribution

It provides a novel realization of cylindric diagrams within affine root systems and characterizes their poset structure and order ideals in terms of Weyl group intervals.

Findings

Cylindric diagrams can be embedded into root systems of type A^{(1)}.

Order ideals correspond to weak Bruhat intervals in the Weyl group.

The paper offers new characterizations of the poset structure of cylindric diagrams.

Abstract

The purpose of the present paper is to give a realization of a cylindric diagram as a subset of root systems of type $A_{\kappa-1}^{(1)}$ and several characterization of its poset structure. Furthermore, the set of order ideals of a cylindric diagram is described as a weak Bruhat interval of the Weyl group.