Weighted Coxeter graphs and generalized geometric representations of Coxeter groups

被引：8

作者：

Bugaenko, Vadim ^{[1
]}

Cherniavsky, Yonah ^{[1
]}

Nagnibeda, Tatiana ^{[2
]}

Shwartz, Robert ^{[1
]}

机构：

[1] Ariel Univ, Dept Math & Comp Sci, Ariel, Israel

[2] Univ Geneva, Dept Math, CH-1211 Geneva 4, Switzerland

来源：

DISCRETE APPLIED MATHEMATICS | 2015年 / 192卷

基金：

瑞士国家科学基金会;

关键词：

Coxeter groups; Coxeter graphs; Geometric representation; Numbers game; Signed graphs; Weighted graphs; Balanced functions on graphs;

D O I：

10.1016/j.dam.2014.05.012

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We introduce the notion of weighted Coxeter graph and associate to it a certain generalization of the standard geometric representation of a Coxeter group. We prove sufficient conditions for faithfulness and non-faithfulness of such a representation. In the case when the weighted Coxeter graph is balanced we discuss how the generalized geometric representation is related to the numbers game played on the Coxeter graph. (C) 2014 Elsevier B.V. All rights reserved.

引用

页码：17 / 27

页数：11

共 50 条

[31] Coxeter groups, Coxeter monoids and the Bruhat order
Toby Kenney
[J]. Journal of Algebraic Combinatorics, 2014, 39 : 719 - 731
[32] Coxeter groups, Coxeter monoids and the Bruhat order
Kenney, Toby
[J]. JOURNAL OF ALGEBRAIC COMBINATORICS, 2014, 39 (03) : 719 - 731
[33] QUASIHARMONIC POLYNOMIALS FOR COXETER GROUPS AND REPRESENTATIONS OF CHEREDNIK ALGEBRAS
Berenstein, Arkady
Burman, Yurii
[J]. TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 2010, 362 (01) : 229 - 260
[34] Cells and representations of right-angled Coxeter groups
Mikhail Belolipetsky
[J]. Selecta Mathematica, 2004, 10 (3)
[35] Narrow normal subgroups of Coxeter groups and of automorphism groups of Coxeter groups
Paris, Luis
Varghese, Olga
[J]. JOURNAL OF GROUP THEORY, 2024, 27 (02) : 255 - 274
[36] Abstract Young representations for Coxeter groups of type D
Cherniavsky, Yona
[J]. ADVANCES IN APPLIED MATHEMATICS, 2008, 41 (04) : 561 - 583
[37] The spectra of Coxeter graphs
Brouwer, AE
Riebeek, RJ
[J]. JOURNAL OF ALGEBRAIC COMBINATORICS, 1998, 8 (01) : 15 - 28
[38] The Spectra of Coxeter Graphs
A.E. Brouwer
R.J. Riebeek
[J]. Journal of Algebraic Combinatorics, 1998, 8 : 15 - 28
[39] On Coxeter graphs of groups with symplectic 3-transpositions
Sozutov, A., I
Sinitsin, V. M.
[J]. TRUDY INSTITUTA MATEMATIKI I MEKHANIKI URO RAN, 2016, 22 (03): : 251 - 258
[40] Weighted L2-cohomology of coxeter groups
Davis, Michael W.
Dymara, Jan
Januszkiewicz, Tadeusz
Okun, Boris
[J]. GEOMETRY & TOPOLOGY, 2007, 11 : 47 - 138

← 1 2 3 4 5 →