2019/01/10 by Alexander Mang, Mang, Alexander, Moritz Weber +1 · 1 citation
Mathematics · #05A18 (Primary) #20G42 (Secondary) #Advanced Combinatorial Mathematics #Algebraic structures and combinatorial models #Combinatorics (math.CO) #FOS: Mathematics #Graph theory and applications #Quantum Algebra (math.QA)
paper · pdf · doi:10.48550/arxiv.1901.03266
openalex created_date 2018/09/27 · openalex publication_date 2019/01/10 · openalex updated_date 2026/08/01
Within the framework of unitary easy quantum groups, we study an analogue of Brauer's Schur-Weyl approach to the representation theory of the orthogonal group. We consider concrete combinatorial categories whose morphisms are formed by partitions of finite sets into disjoint subsets of cardinality two; the points of these sets are colored black or white. These categories correspond to "half-liberated easy" interpolations between the unitary group and Wang's quantum counterpart. We complete the classification of all such categories demonstrating that the subcategories of a certain natural halfway point are equivalent to additive subsemigroups of the natural numbers; the categories above this halfway point have been classified in a preceding article. We achieve this using combinatorial means exclusively. Our work reveals that the half-liberation procedure is quite different from what was previously known from the orthogonal case.