High dimensional hyperbolic Coxeter groups that virtually fiber
Sign Up to like & getrecommendations! Published in 2025 at "Mathematische Annalen"
DOI: 10.1007/s00208-025-03296-2
Abstract: This paper provides an iterative procedure for constructing hyperbolic Coxeter groups that virtually fiber over $\mathbb{Z}$ that is flexible enough to yield infinitely many isomorphism classes in each virtual cohomological dimension (vcd) $n\geq 2$. Our… read more here.
Keywords: hyperbolic coxeter; coxeter; groups virtually; high dimensional ... See more keywords
Involutions in Coxeter groups
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DOI: 10.1007/s10468-025-10332-x
Abstract: We combinatorially characterize the number cc2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\textrm{cc}_2$$\end{document} of conjugacy classes of involutions in any Coxeter group in terms of higher rank odd graphs. This notion naturally generalizes… read more here.
Keywords: usepackage; coxeter groups; document; involutions coxeter ... See more keywords
Determinants of representations of Coxeter groups
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DOI: 10.1007/s10801-018-0842-2
Abstract: In Ayyer et al. (J Comb Theory Ser A 150:208–232, 2017), the authors characterize the partitions of n whose corresponding representations of $$S_n$$Sn have nontrivial determinant. The present paper extends this work to all irreducible… read more here.
Keywords: representations coxeter; determinants representations; coxeter groups;
Hyperbolic right-angled Coxeter groups with boundaries as a Sierpiński carpet and a Menger curve
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DOI: 10.1016/j.topol.2019.03.024
Abstract: Abstract Let ( W , S ) be a hyperbolic right-angled Coxeter system whose nerve is a 1-dimensional strongly co-connected simplicial complex, where “strongly co-connected” is defined in this paper. Then we provide characterizations of… read more here.
Keywords: hyperbolic right; coxeter groups; coxeter; groups boundaries ... See more keywords
DISTRIBUTION OF ACCUMULATION POINTS OF ROOTS FOR TYPE (n - 1, 1) COXETER GROUPS
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DOI: 10.1017/nmj.2018.5
Abstract: In this paper, we investigate the set of accumulation points of normalized roots of infinite Coxeter groups for certain class of their action. Concretely, we prove the conjecture proposed in [6, Section 3.2] in the… read more here.
Keywords: accumulation; coxeter groups; points roots; accumulation points ... See more keywords
Anti-de Sitter strictly GHC-regular groups which are not lattices
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DOI: 10.1090/tran/7530
Abstract: For $d=4, 5, 6, 7, 8$, we exhibit examples of $\mathrm{AdS}^{d,1}$ strictly GHC-regular groups which are not quasi-isometric to the hyperbolic space $\mathbb{H}^d$, nor to any symmetric space. This provides a negative answer to Question… read more here.
Keywords: regular groups; coxeter groups; strictly ghc; anti sitter ... See more keywords
Punctured Surfaces, Quiver Mutations, and Quotients of Coxeter Groups
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DOI: 10.1093/imrn/rnaf320
Abstract: In [1], Barot and Marsh provided an explicit construction of presentation of a finite Weyl group $W$ by any quiver mutation-equivalent to an orientation of a Dynkin diagram with Weyl group $W$. The construction was… read more here.
Keywords: punctured surfaces; coxeter groups; mutations quotients; quotients coxeter ... See more keywords
Root cycles in Coxeter groups
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DOI: 10.1515/jgth-2023-0027
Abstract: Abstract For an element 𝑤 of a Coxeter group 𝑊, there are two important attributes, namely its length, and its expression as a product of disjoint cycles in its action on Φ, the root system… read more here.
Keywords: mathrm seq; kappa; min; coxeter groups ... See more keywords
Mixed Perverse Sheaves on Flag Varieties for Coxeter Groups
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DOI: 10.4153/cjm-2018-034-0
Abstract: Abstract In this paper we construct an abelian category of mixed perverse sheaves attached to any realization of a Coxeter group, in terms of the associated Elias–Williamson diagrammatic category. This construction extends previous work of… read more here.
Keywords: varieties coxeter; coxeter groups; mixed perverse; sheaves flag ... See more keywords