Results 21 to 30 of about 17,658 (187)
Climbing elements in finite Coxeter groups [PDF]
The Electronic Journal of Combinatorics, 2010 We define the notion of a climbing element in a finite real reflection group relative to a total order on the reflection set and we characterise these elements in the case where the total order arises from a bipartite Coxeter element.
Watt, Colum +2 more
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Sortable elements in infinite Coxeter groups [PDF]
Transactions of the American Mathematical Society, 2011 In a series of previous papers, we studied sortable elements in finite Coxeter groups, and the related Cambrian fans. We applied sortable elements and Cambrian fans to the study of cluster algebras of finite type and the noncrossing partitions associated to Artin groups of finite type.
Reading, Nathan, Speyer, David E.
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On Reflection Orders Compatible with a Coxeter Element [PDF]
, 2014 This article was withdrawn, since the generalized statement that any compatible order below some reflection group element in absolute order is a recursive atom order is wrong. A counterexample is for instance the absolute order interval between the identity and the longest element in $H_3$. The statement for Coxeter elements is probably true.
Henri Mühle
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On Orbits of Order Ideals of Minuscule Posets [PDF]
Discrete Mathematics & Theoretical Computer Science, 2013 An action on order ideals of posets considered by Fon-Der-Flaass is analyzed in the case of posets arising from minuscule representations of complex simple Lie algebras.
David B. Rush, Xiaolin Shi
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A note on non-reduced reflection factorizations of Coxeter elements [PDF]
, 2019 We extend a result of Lewis and Reiner from finite Coxeter groups to all Coxeter groups by showing that two reflection factorizations of a Coxeter element lie in the same Hurwitz orbit if and only if they share the same multiset of conjugacy classes ...
Wegener, Patrick, Yahiatene, Sophiane
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Minimal length elements of finite Coxeter groups [PDF]
Duke Mathematical Journal, 2012 19 ...
He, Xuhua, Nie, Sian
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Cyclically reduced elements in Coxeter groups [PDF]
Annales Scientifiques de l'École Normale Supérieure, 2021 Let $W$ be a Coxeter group. We provide a precise description of the conjugacy classes in $W$, in the spirit of Matsumoto's theorem. This extends to all Coxeter groups an important result on finite Coxeter groups by M. Geck and G. Pfeiffer from 1993. In particular, we describe the cyclically reduced elements of $W$, thereby proving a conjecture of A ...
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Domain walls in 4d N $$ \mathcal{N} $$ = 1 SYM
Journal of High Energy Physics, 2021 4d N $$ \mathcal{N} $$ = 1 super Yang-Mills (SYM) with simply connected gauge group G has h gapped vacua arising from the spontaneously broken discrete R-symmetry, where h is the dual Coxeter number of G.
Diego Delmastro, Jaume Gomis
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Antilinear deformations of Coxeter groups, an application to Calogero models [PDF]
, 2010 We construct complex root spaces remaining invariant under antilinear involutions related to all Coxeter groups. We provide two alternative constructions: One is based on deformations of factors of the Coxeter element and the other based on the ...
Andreas Fring +13 more
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The Enumeration of Coxeter Elements [PDF]
Journal of Algebraic Combinatorics, 1997 Let \(W\) be a Coxeter group with a finite distinguished generator set, \(S\), and Coxeter graph, \(\Gamma\). A Coxeter element of \(W\) is a product of all the generators. Let \(C(W)\) denote the set of Coxeter elements in \(W\). The author shows that \(C(W)\) is in one-to-one correspondence with the set of all acyclic orientations of \(\Gamma\). Let \
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