Systems of subspaces of a unitary space

TL;DR

This paper classifies systems of subspaces within a unitary space based on a given poset, providing explicit classifications where feasible, to understand their structure and relationships.

Contribution

It offers a comprehensive classification of subspace systems for all posets with explicit solutions, advancing the understanding of their structure in unitary spaces.

Findings

Explicit classifications for certain posets

Complete description of subspace systems

Framework for analyzing poset representations

Abstract

For a given poset, we consider its representations by systems of subspaces of a unitary space ordered by inclusion. We classify such systems for all posets for which an explicit classification is possible.