Reinhardt Free Spectrahedra

TL;DR

This paper characterizes Reinhardt-symmetric free spectrahedra using graph theory and shows that automorphisms of certain classes are linear, advancing understanding in operator theory and related applications.

Contribution

It provides a graph-theoretic characterization of Reinhardt free spectrahedra and proves linearity of automorphisms for a specific class, offering new insights into their structure.

Findings

Reinhardt symmetry in free spectrahedra characterized graph-theoretically.

Automorphisms of a simple class of these spectrahedra are linear.

Connections established between spectrahedral symmetry and operator theory.

Abstract

Free spectrahedra are natural objects in the theories of operator systems and spaces and completely positive maps. They also appear in various engineering applications. In this paper, free spectrahedra satisfying a Reinhardt symmetry condition are characterized graph theoretically. It is also shown that, for a simple class of such spectrahedra, automorphisms are linear.