Unitarization of linear representations of non-primitive posets

TL;DR

This paper establishes a correspondence between finite types of linear and Hilbert representations of non-primitive posets, showing that indecomposable representations can be unitarized with weights.

Contribution

It proves the equivalence of finiteness of indecomposable linear and Hilbert representations for non-primitive posets and demonstrates unitarization of indecomposable finite-type representations.

Findings

Finite number of indecomposable Hilbert representations corresponds to finite indecomposable linear representations.

Each finite-type indecomposable representation can be unitarized with an appropriate weight.

The results connect the structure of linear and Hilbert representations of non-primitive posets.

Abstract

We prove that partially ordered set has finite number of finite-dimensional indecomposable nonequivalent Hilbert representations with orthoscalarity condition if and anly if it has finite number of indecomposable linear representations. We show that each indecomposable representation of the poset of finite type could be unitarized with some weight.