Results 11 to 20 of about 15,709 (204)
Auslander-Reiten quivers and the Coxeter complex [PDF]
Algebras and Representation Theory, 2002 Let Q be a quiver of type ADE. We construct the corresponding Auslander-Reiten quiver as a topological complex inside the Coxeter complex associated with the underlying Dynkin diagram. We use the notion of chamber weights coming from the theory of the canonical basis of quantized envelopping algebras, and show this set has a special linearity property ...
Shmuel Zelikson
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Subword complexes in Coxeter groups [PDF]
Advances in Mathematics, 2003 Let ( , ) be a Coxeter system. An ordered list of elements in and an element in determine a {\em subword complex}, as introduced in our paper on Gr bner geometry of Schubert polynomials (math.AG/0110058). Subword complexes are demonstrated here to be homeomorphic to balls or spheres, and their Hilbert series are shown to reflect combinatorial ...
Allen Knutson, Ezra Miller
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Coxeter Complexes and Graph-Associahedra [PDF]
Topology and its Applications, 2004 18 pages, 9 figures; revised content and ...
Michael Carr, Satyan L. Devadoss
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Coxeter Cochain Complexes [PDF]
Israel Journal of Mathematics, 2012 15 ...
Michael Larsen, Ayelet Lindenstrauss
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Generalized cluster complexes and Coxeter combinatorics [PDF]
, 2005 We introduce and study a family of simplicial complexes associated to an arbitrary finite root system and a nonnegative integer parameter m. For m=1, our construction specializes to the (simplicial) generalized associahedra or, equivalently, to the cluster complexes for the cluster algebras of finite type.
Sergey Fomin, Nathan Reading
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Bergman Complexes, Coxeter Arrangements, and Graph Associahedra [PDF]
, 2005 Tropical varieties play an important role in algebraic geometry. The Bergman complex B(M) and the positive Bergman complex B+(M) of an oriented matroid M generalize to matroids the notions of the tropical variety and positive tropical variety associated to a linear ideal.
Federico Ardila +2 more
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Stratifying the space of barcodes using Coxeter complexes [PDF]
Journal of Applied and Computational Topology, 2022 AbstractEmbeddings of the space of barcodes in Euclidean spaces are unstable due to the permutation of the bars of a barcode. We use tools from geometric group theory to produce a stratification of the space $${\mathcal {B}}_n$$ B n of barcodes with n bars ...
Benjamin Brück, Adélie Garin
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Coxeter systems with two-dimensional Davis-Vinberg complexes [PDF]
Journal of Pure and Applied Algebra, 2004 In this paper, we study Coxeter systems with two-dimensional Davis-Vinberg complexes. We show that for a Coxeter group $W$, if $(W,S)$ and $(W,S')$ are Coxeter systems with two-dimensional Davis-Vinberg complexes, then there exists $S''\subset W$ such that $(W,S'')$ is a Coxeter system which is isomorphic to $(W,S)$ and the sets of reflections in $(W,S'
Tetsuya Hosaka
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Complex crystallographic Coxeter groups and affine root systems [PDF]
Journal of Nonlinear Mathematical Physics, 2006 The classification (up to an isomorphism in the category of affine groups) is given for the complex crystallographic groups \(\Gamma\) generated by reflections and such that \(d\Gamma\), its linear part, is a Coxeter group, i.e., \(d\Gamma\) is generated by ``real'' reflections of order 2.
Joseph Bernstein, Ossip Schwarzman
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COMPLEX GROWTH SERIES OF COXETER SYSTEMS
, 1992 Let \(W\) be a Coxeter group with (finite) set of generators \(S\). The word length is \(l(w) = \text{min}\{r \mid w = s_ 1s_ 2\dots s_ r\), \(s_ i \in S\}\) and the growth series \(W_ S(t) = \sum_{w\in W}t^{l(w)}\). For \(X \subseteq S\) one has the Coxeter group \(W_ X\) generated by \(X\) and the corresponding growth series \(W_ X(t)\). Let \(\Sigma(
Luis Paris
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