On the Partition Approach to Schur-Weyl Duality and Free Quantum Groups

Freslon, Amaury

doi:10.1007/s00031-016-9410-9

Cited by 43 publications

(60 citation statements)

References 53 publications

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“…Thus, the rest of the classification must deal with one-dimensional representations. At the level of categories of partitions, this can be easily translated (see [8,Thm 4.18] for details). Dealing with categories of partitions which are not block-stable is difficult in general and one aim of this subsection is to develop some tools to describe the effects of this lack of blockstability.…”

Section: General Results On Noncrossing Partition Quantum Groupsmentioning

confidence: 99%

“…Next we consider a one-block partition π(h 1 ⋯h ℓ , h 1 ⋯h ℓ ) with non-through-block partitions b 1 , ⋯, b ℓ−1 between the points. If p denotes the whole partition and w is its upper colouring, we know by [8,Lem 4.2] and Step 1.…”

Section: Twisted Amalgamationmentioning

confidence: 99%

“…We therefore have a through-block and between the points on each row, a non-through-block partition. As in the proof of [8,Lem 4.2], we can reduce q * q by concatenations until the through-block has only four points left while still being in C. Rotating it then yields…”

Section: Classification III : Even Partitionsmentioning

confidence: 99%

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On two-coloured noncrossing partition quantum groups

Freslon¹

2019

Trans. Amer. Math. Soc.

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We classify compact quantum groups associated to noncrossing partitions coloured with two elements x and y which are their own inverses. Together with the work of P. Tarrago and M. Weber, this completes the classification of all noncrossing partition quantum groups on two colours. We also give some general results on the class of all noncrossing partition quantum groups and suggest some wider classification statements.2010 Mathematics Subject Classification. 20G42, 05E10.

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Section: General Results On Noncrossing Partition Quantum Groupsmentioning

confidence: 99%

Section: Twisted Amalgamationmentioning

confidence: 99%

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On two-coloured noncrossing partition quantum groups

Freslon¹

2019

Trans. Amer. Math. Soc.

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“…There are many interesting twisting questions too in connection with the various generalizations of the easy quantum group formalism, as those in [20], [21].…”

Section: Representation Theorymentioning

confidence: 99%

Higher orbitals of quizzy quantum group actions

Banica

2019

Advances in Applied Mathematics

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The hyperoctahedral group H N is known to have two natural liberations: the "good" one H + N , which is the quantum symmetry group of N segments, and the "bad" oneŌ N , which is the quantum symmetry group of the N -hypercube. We study here this phenomenon, in the general "quizzy" framework, which covers the various liberations and twists of H N , O N . Our results include: (1) an interpretation of the embeddinḡ O N ⊂ S + 2 N , as corresponding to the antisymmetric representation of O N , (2) a study of the liberations of H N , notably with the result < H + N ,Ō N >= O + N , and (3) a comparison of the k-orbitals for the inclusions H N ⊂ H + N and H N ⊂Ō N , for k ∈ N small.2010 Mathematics Subject Classification. 46L65 (46L54).

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“…There are of course several potential extensions to be explored, by using for instance the more general notions from [11,15]. Interesting as well would be to try to understand what an "easy algebraic manifold" should be, independently of the quantum group context.…”

Section: T Banicamentioning

confidence: 99%

Weingarten integration over noncommutative homogeneous spaces

Banica¹

2017

Annales Mathématiques Blaise Pascal

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195-224 (2017) Weingarten integration over noncommutative homogeneous spaces Teodor Banica AbstractWe discuss an extension of the Weingarten formula, to the case of noncommutative homogeneous spaces, under suitable "easiness" assumptions. The spaces that we consider are noncommutative algebraic manifolds, generalizing the spaces of type X = G/H ⊂ C N , with H ⊂ G ⊂ UN being subgroups of the unitary group, subject to certain uniformity conditions. We discuss various axiomatization issues, then we establish the Weingarten formula, and we derive some probabilistic consequences. Intégration de Weingarten sur les espaces homogènes non commutatifsRésumé On présente une extension de la formule d'intégration de Weingarten, pour les espaces homogènes non commutatifs, vérifiant des hypothèses « d'aisance » adéquates. Les espaces qu'on considère sont des variétés algebriques non commutatives, généralisant les espaces du type X = G/H ⊂ C N , avec H ⊂ G ⊂ UN étant des sous-groupes du groupe unitaire, vérifiant certaines conditions d'uniformité. On traite d'abord les questions d'axiomatisation, ensuite on établit la formule de Weingarten, et on finit avec quelques conséquences probabilistes.

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On the Partition Approach to Schur-Weyl Duality and Free Quantum Groups

Cited by 43 publications

References 53 publications

On two-coloured noncrossing partition quantum groups

On two-coloured noncrossing partition quantum groups

Higher orbitals of quizzy quantum group actions

Weingarten integration over noncommutative homogeneous spaces

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