The classification of tensor categories of two-colored noncrossing partitions
Pierre Tarrago,Moritz Weber +1 more
TLDR
In this article, the authors introduced the notion of two-colored noncrossing partitions, which are exactly the tensor categories being used in the theory of easy quantum groups.About:
This article is published in Journal of Combinatorial Theory, Series A.The article was published on 2018-02-01 and is currently open access. It has received 30 citations till now. The article focuses on the topics: Noncrossing partition & Disjoint sets.read more
Citations
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Introduction to compact (matrix) quantum groups and Banica–Speicher (easy) quantum groups
TL;DR: In this article, the authors define Banica-Speicher quantum groups (also called easy quantum groups), a class of compact matrix quantum groups determined by the combinatorics of set partitions.
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Classification of globally colorized categories of partitions
TL;DR: In this paper, a tensor category is defined for set partitions closed under certain operations, which give rise to certain subgroups of the free orthogonal quantum group On+, the so-called easy quantum groups.
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Categories of two-colored pair partitions Part II: Categories indexed by semigroups
Alexander Mang,Moritz Weber +1 more
TL;DR: An analogue of Brauer's Schur-Weyl approach to the representation theory of the orthogonal group is studied, demonstrating that the subcategories of a certain natural halfway point are equivalent to additive subsemigroups of the natural numbers.
Posted Content
Quantum groups based on spatial partitions
Guillaume Cébron,Moritz Weber +1 more
TL;DR: In this paper, the authors define new compact matrix quantum groups whose intertwiner spaces are dual to tensor categories of three-dimensional set partitions, which they call spatial partitions, and give a quantum group interpretation of certain categories of partitions which do neither contain the pair partition nor the identity partition.
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Homogeneous quantum groups and their easiness level
TL;DR: The easiness level of a closed subgroup G⊂UN+ is defined in this paper, where it is shown that the maximal liberation inclusions remain maximal in the easy setting.
References
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Compact matrix pseudogroups
TL;DR: The compact matrix pseudogroup as mentioned in this paper is a non-commutative compact space endowed with a group structure, and the existence and uniqueness of the Haar measure is proved and orthonormality relations for matrix elements of irreducible representations are derived.
Book
Enumerative Combinatorics: Volume 1
TL;DR: The second edition of the Basic Introduction to Enumerative Combinative Analysis as discussed by the authors includes ten new sections and more than 300 new exercises, most with solutions, reflecting numerous new developments since the publication of the first edition in 1986.
Book
Lectures on the Combinatorics of Free Probability
Alexandru Nica,Roland Speicher +1 more
TL;DR: In this article, the authors present a case study of non-normal distribution and non-commutative joint distributions and define a set of basic combinatorics, such as non-crossing partitions, sum-of-free random variables, and products of free random variables.
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Tannaka-Krein duality for compact matrix pseudogroups. Twisted SU(N) groups
TL;DR: In this paper, the notion of concrete monoidal W *-category is introduced and investigated, and a generalization of the Tannaka-Krein duality theorem is proved, leading to new examples of compact matrix pseudogroups.
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Liberation of orthogonal Lie groups
Teodor Banica,Roland Speicher +1 more
TL;DR: In this paper, it was shown that under suitable assumptions, there is a one-to-one correspondence between classical groups and free quantum groups, in the compact orthogonal case.