Classification results for easy quantum groups

TL;DR

This paper investigates a class of orthogonal quantum groups called easy quantum groups, introduces new examples, and explores their structure and character laws, aiming to classify all such groups.

Contribution

It provides new examples of easy quantum groups, partial classification results, and insights into their structure and asymptotic character laws.

Findings

Identification of new easy quantum groups

Partial classification supporting the conjecture

Computation of asymptotic character laws

Abstract

We study the orthogonal quantum groups satisfying the ``easiness'' assumption axiomatized in our previous paper, with the construction of some new examples, and with some partial classification results. The conjectural conclusion is that the easy quantum groups consist of the previously known 14 examples, plus of an hypothetical multi-parameter ``hyperoctahedral series'', related to the complex reflection groups $H_n^s=\mathbb Z_s\wr S_n$. We discuss as well the general structure, and the computation of asymptotic laws of characters, for the new quantum groups that we construct.