منابع مشابه
Coxeter Covers of the Classical Coxeter Groups
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...
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 ...
متن کاملThe double Coxeter arrangement
Let V be Euclidean space. Let W ⊂ GL(V ) be a finite irreducible reflection group. Let A be the corresponding Coxeter arrangement. Let S be the algebra of polynomial functions on V. For H ∈ A choose αH ∈ V ∗ such that H = ker(αH). The arrangement A is known to be free: the derivation module D(A) = {θ ∈ DerS | θ(αH ) ∈ SαH} is a free S-module with generators of degrees equal to the exponents of ...
متن کاملCoxeter Theory: The Cognitive Aspects
Coxeter Theory is a fascinating example of a mathematical theory where the cognitive roots of mathematical thinking are directly evident. The paper contains an informal discussion, made from a mathematician’s point of view, of possible cognitive aspects of the theory. We hope that it will be interesting to mathematicians and cognitive scientists alike.
متن کاملThe Enumeration of Coxeter Elements
Let (W, S, 0) be a Coxeter system: a Coxeter group W with S its distinguished generator set and 0 its Coxeter graph. In the present paper, we always assume that the cardinality l = |S| of S is finite. A Coxeter element of W is by definition a product of all generators s ∈ S in any fixed order. We use the notation C(W ) to denote the set of all the Coxeter elements in W . These elements play an ...
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ژورنال
عنوان ژورنال: International Journal of Mathematics and Mathematical Sciences
سال: 2000
ISSN: 0161-1712,1687-0425
DOI: 10.1155/s0161171200002167