On the twist conjecture for Coxeter groups
نویسندگان
چکیده
منابع مشابه
On the three-dimensional Singer Conjecture for Coxeter groups
We give a proof of the Singer conjecture (on the vanishing of reduced l-homology except in the middle dimension) for the Davis Complex Σ associated to a Coxeter system (W,S) whose nerve L is a triangulation of S . We show that it follows from a theorem of Andreev, which gives the necessary and sufficient conditions for a classical reflection group to act on H.
متن کاملEssays on Coxeter groups Coxeter elements in finite Coxeter groups
A finite Coxeter group possesses a distinguished conjugacy class of Coxeter elements. The literature about these is very large, but it seems to me that there is still room for a better motivated account than what exists. The standard references on thismaterial are [Bourbaki:1968] and [Humphreys:1990], butmy treatment follows [Steinberg:1959] and [Steinberg:1985], from which the clever parts of ...
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Let W be a crystallographic group with its a-function upper bounded. In [15], the author showed that if x ∼ L y in W then R(x) = R(y) and Σ(x) = Σ(y), and conjectured that the reverse conclusion should also be true. In the present paper, we show this conjecture in the cases when W is an irreducible Weyl group W ′ and when W is an irreducible affine Weyl group Wa with the following cases excepte...
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It is shown that the outer automorphism group of a Coxeter group W of nite rank is nite if the Coxeter graph contains no innnite bonds. A key step in the proof is to show that if the group is irreducible and 1 and 2 any two bases of the root system of W, then 2 = w 1 for some w 2 W. The proof of this latter fact employs some properties of the dominance order on the root system introduced by Bri...
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Let C(T ) be a generalized Coxeter group, which has a natural map onto one of the classical Coxeter groups, either Bn or Dn. Let CY (T ) be a natural quotient of C(T ), and if C(T ) is simply-laced (which means all the relations between the generators has order 2 or 3), CY (T ) is a generalized Coxeter group, too . Let At,n be a group which contains t Abelian groups generated by n elements. The...
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ژورنال
عنوان ژورنال: Innovations in Incidence Geometry: Algebraic, Topological and Combinatorial
سال: 2011
ISSN: 2640-7345,2640-7337
DOI: 10.2140/iig.2011.12.111