Marked chain-order polytopes

TL;DR

This paper introduces marked chain-order polytopes, a new family of polytopes generalizing existing ones, with applications in representation theory and combinatorics.

Contribution

It defines marked chain-order polytopes, explores their properties, and connects them to Ehrhart theory and PBW degenerations in Lie algebra representations.

Findings

Marked chain-order polytopes unify chain and order polytopes as extremal cases.

The polytopes are Ehrhart equivalent within their family.

Applications to PBW degenerations in Lie algebra representations.

Abstract

We introduce in this paper the marked chain-order polytopes associated to a marked poset, generalizing the marked chain polytopes and marked order polytopes by putting them as extremal cases in an Ehrhart equivalent family. Some combinatorial properties of these polytopes are studied. This work is motivated by the framework of PBW degenerations in representation theory of Lie algebras.