On the Hurwitz action in affine Coxeter groups

Wegener, Patrick

doi:10.1016/j.jpaa.2020.106308

Cited by 7 publications

(13 citation statements)

References 27 publications

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“…Now we can answer the question above. Recently, Wegener showed that the dual Matsumoto property holds for quasi-Coxeter elements in affine Coxeter systems as well [53]. These two results have the following consequence.…”

Section: The Hurwitz Actionmentioning

confidence: 85%

Non-crossing partitions

Baumeister¹,

Bux²,

Götze³

et al. 2019

EMS Series of Congress Reports

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Non-crossing partitions have been a staple in combinatorics for quite some time. More recently, they have surfaced (sometimes unexpectedly) in various other contexts from free probability to classifying spaces of braid groups. Also, analogues of the non-crossing partition lattice have been introduced. Here, the classical non-crossing partitions are associated to Coxeter and Artin groups of type An, which explains the tight connection to the symmetric groups and braid groups. We shall outline those developments.

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Section: The Hurwitz Actionmentioning

confidence: 85%

Non-crossing partitions

Baumeister¹,

Bux²,

Götze³

et al. 2019

EMS Series of Congress Reports

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“…Now we prove Theorem 1.4 which investigates uniformly the Hurwitz action on the set of reduced reflection factorizations of parabolic quasi-Coxeter elements in Weyl groups. It is already proven case-based in [2] for finite Coxeter groups ae well as partially for simply laced Weyl groups in [24] and also case-based for affine Coxeter groups in [25].…”

Section: Theorem 13 Provides a Characterization Of Maximal Parabolic Quasi-coxeter Elements Inmentioning

confidence: 98%

A note on non-reduced reflection factorizations of Coxeter elements

Wegener¹,

Yahiatene²

2020

Algebraic Combinatorics

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“…The Hurwitz action on closed intervals in (G, ≤ T ) was recently studied in [30]. For specific groups, the Hurwitz action was studied for instance in [5,6,8,14,16,34,39].…”

Section: Introductionmentioning

confidence: 99%

A poset structure on the alternating group generated by 3-cycles

Muehle¹,

Nadeau²

2019

Algebraic Combinatorics

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We investigate the poset structure on the alternating group that arises when the latter is generated by 3-cycles. We study intervals in this poset and give several enumerative results, as well as a complete description of the orbits of the Hurwitz action on maximal chains. Our motivating example is the well-studied absolute order arising when the symmetric group is generated by transpositions, i.e. 2-cycles, and we compare our results to this case along the way. In particular, noncrossing partitions arise naturally in both settings.2010 Mathematics Subject Classification. 06A07 (primary), and 05A10, 05E15, 20B35 (secondary).

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On the Hurwitz action in affine Coxeter groups

Cited by 7 publications

References 27 publications

Non-crossing partitions

Non-crossing partitions

A note on non-reduced reflection factorizations of Coxeter elements

A poset structure on the alternating group generated by 3-cycles

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