Conjugation Properties of Tensor Product and Fusion Coefficients

TL;DR

This paper reviews recent findings on how tensor product and fusion coefficients behave under complex conjugation, highlighting proven results, conjectures, and new observations in representation theory of finite simple groups of Lie type.

Contribution

It presents new conjectures and observations on the conjugation properties of tensor and fusion coefficients, including insights into finite simple groups of Lie type.

Findings

Some properties are proven, others remain conjectural.

New observations on representation theory of finite simple groups of Lie type.

Identifies open problems and directions for future research.

Abstract

We review some recent results on properties of tensor product and fusion coefficients under complex conjugation of one of the factors. Some of these results have been proven, some others are conjectures awaiting a proof, one of them involving hitherto unnoticed observations on ordinary representation theory of finite simple groups of Lie type