Bolytrope orders

TL;DR

This paper introduces bolytropes as bounded subsets in affine buildings and establishes a correspondence between bolytropes and bolytrope orders, extending known relations between polytropes and graduated orders.

Contribution

It generalizes the polytrope-graduated order correspondence to bolytropes and bolytrope orders within affine buildings.

Findings

Bolytropes are characterized as bounded subsets with specific distance properties.

Points of a bolytrope correspond to invariant lattices of a bolytrope order.

The work extends the polytrope-graduated order relationship to a broader setting.

Abstract

Bolytropes are bounded subsets of an affine building that consist of all points that have distance at most $r$ from some polytrope. We prove that the points of a bolytrope describe the set of all invariant lattices of a bolytrope order, generalizing the correspondence between polytropes and graduated orders.