Weighted Coxeter graphs and generalized geometric representations of Coxeter groups
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چکیده
منابع مشابه
Roots of asymmetric geometric representations of Coxeter groups
X iv :0 70 7. 33 10 v2 [ m at h. G R ] 3 0 Se p 20 07 Roots of asymmetric geometric representations of Coxeter groups Robert G. Donnelly1 Department of Mathematics and Statistics, Murray State University, Murray, KY 42071 Abstract Results are obtained concerning the roots of asymmetric geometric representations of Coxeter groups. These representations were independently introduced by Vinberg an...
متن کاملRoot systems for asymmetric geometric representations of Coxeter groups
Root systems for asymmetric geometric representations of Coxeter groups Robert G. Donnelly1 Department of Mathematics and Statistics, Murray State University, Murray, KY 42071 Abstract Results are obtained concerning root systems for asymmetric geometric representations of Coxeter groups. These representations were independently introduced by Vinberg and Eriksson, and generalize the standard ge...
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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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In [APS17], the authors characterize the partitions of n whose corresponding representations of Sn have nontrivial determinant. The present paper extends this work to all irreducible finite Coxeter groups W . Namely, given a nontrivial multiplicative character ω of W , we give a closed formula for the number of irreducible representations of W with determinant ω. For Coxeter groups of type Bn a...
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Given a Coxeter system .W;S/ and a positive real multiparameter q , we study the “weighted L–cohomology groups,” of a certain simplicial complex † associated to .W;S/ . These cohomology groups are Hilbert spaces, as well as modules over the Hecke algebra associated to .W;S/ and the multiparameter q . They have a “von Neumann dimension” with respect to the associated “Hecke–von Neumann algebra” ...
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ژورنال
عنوان ژورنال: Discrete Applied Mathematics
سال: 2015
ISSN: 0166-218X
DOI: 10.1016/j.dam.2014.05.012