Representations of posets: Linear versus Unitary

TL;DR

This paper explores the relationship between the representation theories of posets in linear and unitary spaces, revealing that results in the unitary case closely mirror those in the classical linear case.

Contribution

It provides insights into the connection between linear and unitary representations of posets, highlighting the similarities and differences in their theoretical frameworks.

Findings

Results in the unitary case are well-correlated with the linear case

The paper clarifies the phenomena linking the two representation theories

It sheds light on the generalization of classical linear theory to the unitary setting

Abstract

A number of recent papers treated the representation theory of partially ordered sets in unitary spaces with the so called orthoscalar relation. Such theory generalizes the classical theory which studies the representations of partially ordered sets in linear spaces. It happens that the results in the unitary case are well-correlated with those in the linear case. The purpose of this article is to shed light on this phenomena.