On the Hurwitz action in finite Coxeter groups

Baumeister, Barbara; Gobet, Thomas; Roberts, Kieran; Wegener, Patrick

doi:10.1515/jgth-2016-0025

Cited by 23 publications

(80 citation statements)

References 31 publications

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“…See for more on the topic. Remark There are several (unequivalent) definitions of Coxeter elements (see for instance [, Section 2.2]). The above definitions still make sense for more general Coxeter elements, but for the realization of the dual braid monoids (which are introduced in the next section) inside Artin groups the Coxeter element is required to be standard (see [, Remark 5.11]).…”

Section: Dual Braid Monoidsmentioning

confidence: 99%

Simple dual braids, noncrossing partitions and Mikado braids of type Dn

Baumeister

Gobet

2017

Bull. London Math. Soc.

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We show that the simple elements of the dual Garside structure of an Artin group of type Dn are Mikado braids, giving a positive answer to a conjecture of Digne and the second author. To this end, we use an embedding of the Artin group of type Dn in a suitable quotient of an Artin group of type Bn noted by Allcock, of which we give a simple algebraic proof here. This allows one to give a characterization of the Mikado braids of type Dn in terms of those of type Bn and also to describe them topologically. Using this topological representation and Athanasiadis and Reiner's model for noncrossing partitions of type Dn which can be used to represent the simple elements, we deduce the above‐mentioned conjecture.

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Section: Dual Braid Monoidsmentioning

confidence: 99%

Simple dual braids, noncrossing partitions and Mikado braids of type Dn

Baumeister

Gobet

2017

Bull. London Math. Soc.

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“…In [BGRW17] the authors provided a necessary and sufficient condition on an element of a finite Coxeter group to ensure the transitivity of the Hurwitz action on its set of reduced reflection decompositions. An element of a Coxeter group is called a parabolic quasi-Coxeter element if it admits a reduced reflection decomposition which generates a parabolic subgroup.…”

Section: Introductionmentioning

confidence: 99%

On the Hurwitz action in affine Coxeter groups

Wegener

2020

Journal of Pure and Applied Algebra

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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 finite Coxeter groups

Cited by 23 publications

References 31 publications

Simple dual braids, noncrossing partitions and Mikado braids of type Dn

Simple dual braids, noncrossing partitions and Mikado braids of type Dn

On the Hurwitz action in affine Coxeter groups

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

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