Results 81 to 90 of about 2,366 (219)

Cells in Coxeter groups, I

Journal of Algebra, 2013
The purpose of this article is to shed new light on the combinatorial structure of Kazhdan-Lusztig cells in infinite Coxeter groups $W$. Our main focus is the set $\D$ of distinguished involutions in $W$, which was introduced by Lusztig in one of his first papers on cells in affine Weyl groups.
Belolipetsky, M, Gunnells, PE
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Presentations of the braid group of the complex reflection group G(d,d,n)$G(d,d,n)$

Journal of the London Mathematical Society, Volume 113, Issue 4, April 2026.
Abstract We show that the braid group associated to the complex reflection group G(d,d,n)$G(d,d,n)$ is an index d$d$ subgroup of the braid group of the orbifold quotient of the complex numbers by a cyclic group of order d$d$. We also give a compatible presentation of G(d,d,n)$G(d,d,n)$ and its braid group for each tagged triangulation of the disk with ...
Francesca Fedele, Bethany Rose Marsh
wiley   +1 more source

Conjugacy of Coxeter elements [PDF]

, 2009
For a Coxeter group (W, S), a permutation of the set S is called a Coxeter word and the group element represented by the product is called a Coxeter element. Moving the first letter to the end of the word is called a rotation and two Coxeter elements are
Eriksson, Henrik,, Eriksson, Kimmo,
core  

Abstract reflections and Coxeter groups [PDF]

, 1977
A notion of “abstract reflection” is introduced and used to characterize the Coxeter groups. Several known results on Coxeter groups are obtained as easy corollaries.
David M. Goldschmidt
core   +1 more source

Subword Complexes and Nil-Hecke Moves

Моделирование и анализ информационных систем, 2013
For a finite Coxeter group W, a subword complex is a simplicial complex associated with a pair (Q, ρ), where Q is a word in the alphabet of simple reflections, ρ is a group element.
M. A. Gorsky
doaj   +1 more source

k-Parabolic Subspace Arrangements [PDF]

Discrete Mathematics & Theoretical Computer Science, 2009
In this paper, we study k-parabolic arrangements, a generalization of the k-equal arrangement for any finite real reflection group. When k=2, these arrangements correspond to the well-studied Coxeter arrangements.
Christopher Severs, Jacob White
doaj   +1 more source

On a duality in Coxeter groups

European Journal of Combinatorics, 2008
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Variants of a theorem of Macbeath in finite‐dimensional normed spaces

Mathematika, Volume 72, Issue 2, April 2026.
Abstract A classical theorem of Macbeath states that for any integers d⩾2$d \geqslant 2$, n⩾d+1$n \geqslant d+1$, d$d$‐dimensional Euclidean balls are hardest to approximate, in terms of volume difference, by inscribed convex polytopes with n$n$ vertices.
Zsolt Lángi, Shanshan Wang
wiley   +1 more source

Linearized Coxeter higher-spin theories

Journal of High Energy Physics
A class of higher-spin gauge theories on AdS 4 associated with various Coxeter groups C $$ \mathcal{C} $$ is analyzed at the linear order. For a general C $$ \mathcal{C} $$ , a solution corresponding to the AdS 4 space and the form of the free unfolded ...
A. A. Tarusov, K. A. Ushakov, M. A. Vasiliev   +2 more
doaj   +1 more source

On Minimal Covolume Hyperbolic Lattices

Mathematics, 2017
We study lattices with a non-compact fundamental domain of small volume in hyperbolic space H n . First, we identify the arithmetic lattices in Isom + H n of minimal covolume for even n up to 18.
Ruth Kellerhals
doaj   +1 more source