Results 21 to 30 of about 21,101 (195)
Shortest path poset of finite Coxeter groups [PDF]
Discrete Mathematics & Theoretical Computer Science, 2009 We define a poset using the shortest paths in the Bruhat graph of a finite Coxeter group $W$ from the identity to the longest word in $W, w_0$. We show that this poset is the union of Boolean posets of rank absolute length of $w_0$; that is, any shortest
Saúl A. Blanco
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On the direct indecomposability of infinite irreducible Coxeter groups and the Isomorphism Problem of Coxeter groups [PDF]
, 2005 In this paper we prove, without the finite rank assumption, that any irreducible Coxeter group of infinite order is directly indecomposable as an abstract group.
Brink B. +6 more
core +1 more source
Geometriae Dedicata, 2008 A solution of the isomorphism problem is presented for the class of Coxeter groups W that have a finite set of Coxeter generators S such that the underlying graph of the presentation diagram of the system (W,S) has the property that every cycle of length at least four has a cord.
Ratcliffe, John G., Tschantz, Steven T.
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A Special Class of Rank 10 and 11 Coxeter Groups [PDF]
, 2006 In the course of investigating regular subalgebras of E(10) related to cosmological solutions of 11-dimensional supergravity supporting an electric 4-form field, a class of rank 10 Coxeter subgroups of the Weyl group of E(10) was uncovered (hep-th ...
Daniel Persson +5 more
core +7 more sources
IRREDUCIBLE COXETER GROUPS [PDF]
International Journal of Algebra and Computation, 2007 We prove that a non-spherical irreducible Coxeter group is (directly) indecomposable and that an indefinite irreducible Coxeter group is strongly indecomposable in the sense that all its finite index subgroups are (directly) indecomposable. Let W be a Coxeter group.
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Coxeter groups and the PMNS matrix
European Physical Journal C: Particles and Fields, 2017 We discuss symmetries of the Lagrangian of the leptonic sector. We consider the case when this symmetry group is a Coxeter group, and identify the low energy residual symmetries with the involution generators, i.e., generators with order equal to 2.
Pritibhajan Byakti, Palash B. Pal
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Fully commutative elements and lattice walks [PDF]
Discrete Mathematics & Theoretical Computer Science, 2013 An element of a Coxeter group $W$ is fully commutative if any two of its reduced decompositions are related by a series of transpositions of adjacent commuting generators. These elements were extensively studied by Stembridge in the finite case.
Riccardo Biagioli +2 more
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PT-symmetric deformations of Calogero models [PDF]
, 2008 We demonstrate that Coxeter groups allow for complex PT-symmetric deformations across the boundaries of all Weyl chambers. We compute the explicit deformations for the A2 and G2-Coxeter group and apply these constructions to Calogero–Moser–Sutherland ...
Andreas Fring +18 more
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Automorphisms of Right-Angled Coxeter Groups
International Journal of Mathematics and Mathematical Sciences, 2008 If (𝑊,𝑆) is a right-angled Coxeter system, then Aut(𝑊) is a semidirect product of the group Aut∘(𝑊) of symmetric automorphisms by the automorphism group of a certain groupoid. We show that, under mild conditions, Aut∘(𝑊) is a semidirect product of Inn(𝑊)
Mauricio Gutierrez, Anton Kaul
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Asymptotical behaviour of roots of infinite Coxeter groups I [PDF]
Discrete Mathematics & Theoretical Computer Science, 2012 Let $W$ be an infinite Coxeter group, and $\Phi$ be the root system constructed from its geometric representation. We study the set $E$ of limit points of "normalized'' roots (representing the directions of the roots).
Christophe Hohlweg +2 more
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