نتایج جستجو برای: coxeter system

تعداد نتایج: 2232874  

2010
PETER A. BROOKSBANK ADAM PIGGOTT

We characterize certain properties of the derived series of Coxeter groups by properties of the corresponding Coxeter graphs. In particular, we give necessary and sufficient conditions for a Coxeter group to be quasiperfect.

2005
Sergey Fomin Nathan Reading

In the first part of this paper (Sections 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, and 12), we introduce and study a simplicial complex ∆(Φ) associated to a finite root system Φ and a nonnegative integer parameter m. For m = 1, our construction specializes to the (simplicial) generalized associahedra ∆(Φ) introduced in [13] and identified in [14] as the underlying complexes for the cluster algebras of f...

Journal: :International Journal of Algebra and Computation 2010

2008
KOJI NUIDA

In this paper we prove that any irreducible Coxeter group of infinite order is directly indecomposable as an abstract group, without the finite rank assumption. The key ingredient of the proof is that we can determine, for an irreducible Coxeter group W , the centralizers in W of the normal subgroups of W that are generated by involutions. As a consequence, we show that the problem of deciding ...

2004
P. V. TUMARKIN

Noncompact hyperbolic Coxeter n-polytopes of finite volume and having n+ 3 facets are studied in this paper. Unlike the spherical and parabolic cases, no complete classification exists as yet for hyperbolic Coxeter polytopes of finite volume. It has been shown that the dimension of a bounded Coxeter polytope is at most 29 (Vinberg, 1984), while an upper estimate in the unbounded case is 995 (Pr...

2002
Richard F. Booth Alexandre V. Borovik Neil White

Coxeter matroids are combinatorial objects associated with finite Coxeter groups; they can be viewed as subsets M of the factor set W/P of a Coxeter group W by a parabolic subgroup P which satisfy a certain maximality property with respect to a family of shifted Bruhat orders on W/P . The classical matroids of matroid theory are exactly the Coxeter matroids for the symmetric group Symn (which i...

2009
MARK COLARUSSO M. COLARUSSO

In recent work ([9],[10]), Kostant and Wallach construct an action of a simply connected Lie group A ≃ C( n 2 ) on gl(n) using a completely integrable system derived from the Poisson analogue of the Gelfand-Zeitlin subalgebra of the enveloping algebra. In [9], the authors show that A-orbits of dimension ( n 2 ) form Lagrangian submanifolds of regular adjoint orbits in gl(n). They describe the o...

2010
Frédéric Haglund Daniel T. Wise Henning Krause

In this paper we prove that every finitely generated Coxeter group has a finite index subgroup that is the fundamental group of a special cube complex. Some consequences include: Every f.g. Coxeter group is virtually a subgroup of a right-angled Coxeter group. Every word-hyperbolic Coxeter group has separable quasiconvex subgroups. © 2010 Elsevier Inc. All rights reserved. MSC: 53C23; 20F36; 20...

Journal: :Eur. J. Comb. 2017
Matthieu Jacquemet

Beside simplices, n-cubes form an important class of simple polyhedra. Unlike hyperbolic Coxeter simplices, hyperbolic Coxeter n-cubes are not classified. In this work, we first show that there are no Coxeter n-cubes in H for n ≥ 10. Then, we show that the ideal ones exist only for n = 2 and 3, and provide a classification. The methods used are of combinatorial and algebraic nature, using prope...

2007
Jian-yi Shi

By the correspondence between Coxeter elements of a Coxeter system (W, S, Γ) and the acyclic orientations of the Coxeter graph Γ, we study some properties of elements in the set C0(W ). We show that when W is of finite, affine or hyperbolic type, any w ∈ C0(W ) satisfies w ∼ LR wJ with `(wJ ) = |J | = m(w) for some J ⊂ S. Now assume that W is of finite or affine type. We give an explicit descri...

نمودار تعداد نتایج جستجو در هر سال

با کلیک روی نمودار نتایج را به سال انتشار فیلتر کنید