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

2020/03/01 by Mang, Alexander, Weber, Moritz
#05A18 (Primary) #20G42 (Secondary) #Combinatorics (math.CO) #FOS: Mathematics #Quantum Algebra (math.QA)

paper · doi:10.48550/arxiv.2003.00569

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 co-representation categories of a specific class of quantum groups. However, our series of articles is purely combinatorial. 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.

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• Categories of Two-Colored Pair Partitions, Part II: Categories Indexed by Semigroups
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