Non-hyperoctahedral Categories of Two-Colored Partitions Part II: All Possible Parameter Values

Abstract

This article is part of a series with the aim of classifying all non-hyperoctahedral categories of two-colored partitions. Those constitute by some Tannaka-Krein type result the representation categories of a specific class of quantum groups. In Part I we introduced a class of parameters which gave rise to many new non-hyperoctahedral categories of partitions. In the present article we show that this class actually contains all possible parameter values of all non hyperoctahedral categories of partitions. This is an important step towards the classification of all non-hyperoctahedral categories.