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On the direct indecomposability of infinite irreducible Coxeter groups and the Isomorphism Problem of Coxeter groups [PDF]
, 2005 In this paper we prove, without the finite rank assumption, that any irreducible Coxeter group of infinite order is directly indecomposable as an abstract group.
Brink B. +6 more
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Arithmetic of arithmetic Coxeter groups. [PDF]
Proc Natl Acad Sci U S A, 2019 In the 1990s, J.H. Conway published a combinatorial-geometric method for analyzing integer-valued binary quadratic forms (BQFs). Using a visualization he named the "topograph," Conway revisited the reduction of BQFs and the solution of quadratic ...
Milea S, Shelley CD, Weissman MH.
europepmc +2 more sources
Discrete Mathematics & Theoretical Computer Science, 2004 Motivated by the Coxeter complex associated to a Coxeter system (W,S), we introduce a simplicial regular cell complex Δ(G,S) with a G-action associated to any pair (G,S) where G is a group and S is a finite set of generators for G which is ...
Eric Babson, Victor Reiner
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On non-conjugate Coxeter elements in well-generated reflection groups [PDF]
Discrete Mathematics & Theoretical Computer Science, 2015 Given an irreducible well-generated complex reflection group $W$ with Coxeter number $h$, we call a Coxeter element any regular element (in the sense of Springer) of order $h$ in $W$; this is a slight extension of the most common notion of Coxeter ...
Victor Reiner +2 more
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Interval groups related to finite Coxeter groups Part II
Transactions of the London Mathematical Society, 2023 We provide a complete description of the presentations of the interval groups related to quasi‐Coxeter elements in finite Coxeter groups. In the simply laced cases, we show that each interval group is the quotient of the Artin group associated with the ...
Barbara Baumeister +3 more
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Parabolic double cosets in Coxeter groups [PDF]
Discrete Mathematics & Theoretical Computer Science, 2020 Parabolic subgroups WI of Coxeter systems (W,S) and their ordinary and double cosets W/WI and WI\W/WJ appear in many contexts in combinatorics and Lie theory, including the geometry and topology of generalized flag varieties and the symmetry groups of ...
Sara Billey +4 more
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A two-sided analogue of the Coxeter complex [PDF]
Discrete Mathematics & Theoretical Computer Science, 2020 For any Coxeter system (W, S) of rank n, we introduce an abstract boolean complex (simplicial poset) of dimension 2n − 1 which contains the Coxeter complex as a relative subcomplex.
T. Kyle Petersen
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Kazhdan-Lusztig polynomials of boolean elements [PDF]
Discrete Mathematics & Theoretical Computer Science, 2013 We give closed combinatorial product formulas for Kazhdan–Lusztig poynomials and their parabolic analogue of type $q$ in the case of boolean elements, introduced in [M. Marietti, Boolean elements in Kazhdan–Lusztig theory, J.
Pietro Mongelli
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Fully commutative elements and lattice walks [PDF]
Discrete Mathematics & Theoretical Computer Science, 2013 An element of a Coxeter group $W$ is fully commutative if any two of its reduced decompositions are related by a series of transpositions of adjacent commuting generators. These elements were extensively studied by Stembridge in the finite case.
Riccardo Biagioli +2 more
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k-Parabolic Subspace Arrangements [PDF]
Discrete Mathematics & Theoretical Computer Science, 2009 In this paper, we study k-parabolic arrangements, a generalization of the k-equal arrangement for any finite real reflection group. When k=2, these arrangements correspond to the well-studied Coxeter arrangements.
Christopher Severs, Jacob White
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