Quantum permutations, Hadamard matrices, and the search for matrix models

TL;DR

This paper explores the relationships between quantum permutation groups and complex Hadamard matrices, presenting recent findings, open problems, and conjectures about matrix models in this mathematical framework.

Contribution

It introduces new connections between quantum permutation groups and Hadamard matrices, along with a comprehensive list of open problems and conjectural ideas about matrix models.

Findings

Established links between quantum permutation groups and Hadamard matrices

Presented a list of open problems in the field

Proposed conjectural statements regarding matrix models

Abstract

This is a presentation of recent work on quantum permutation groups, complex Hadamard matrices, and the connections between them. A long list of problems is included. We include as well some conjectural statements, about matrix models.