Results 11 to 20 of about 304 (161)
A primitive derivation and logarithmic differential forms of Coxeter arrangements [PDF]
Mathematische Zeitschrift, 2009 Let $W$ be a finite irreducible real reflection group, which is a Coxeter group. We explicitly construct a basis for the module of differential 1-forms with logarithmic poles along the Coxeter arrangement by using a primitive derivation. As a consequence, we extend the Hodge filtration, indexed by nonnegative integers, into a filtration indexed by all ...
Takuro Abe, Hiroaki Terao
exaly +8 more sources
Equivariant multiplicities of Coxeter arrangements and invariant bases [PDF]
Advances in Mathematics, 2012 Let $\A$ be an irreducible Coxeter arrangement and $W$ be its Coxeter group. Then $W$ naturally acts on $\A$. A multiplicity $\bfm : \A\rightarrow \Z$ is said to be equivariant when $\bfm$ is constant on each $W$-orbit of $\A$. In this article, we prove that the multi-derivation module $D(\A, \bfm)$ is a free module whenever $\bfm$ is equivariant by ...
Takuro Abe, Hiroaki Terao
exaly +6 more sources
Partial Normalizations of Coxeter Arrangements and Discriminants [PDF]
Moscow Mathematical Journal, 2012 24 pages, 1 figure, amended ...
Granger, Michel +2 more
core +6 more sources
The double Coxeter arrangement [PDF]
Commentarii Mathematici Helvetici, 1998 Consider a finite collection \(\mathcal A\) of linear hyperplanes in \({\mathbb R}^\ell\). Let \(\alpha_H: {\mathbb R}^\ell \to {\mathbb R}\) satisfy \(H=\ker \alpha_H\), for \(H\in {\mathcal A}\). Let \(S={\mathbb R}[x_1,\ldots,x_\ell]\). A derivation \(\theta\) of \(S\) is tangent along \(\mathcal A\) if \(\theta(\alpha_H)\) is a multiple of ...
Solomon, L., Terao, H.
openaire +5 more sources
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
doaj +2 more sources
On the invariants of the cohomology of complements of Coxeter arrangements
Journal of Algebra, 2020 We refine Brieskorn's study of the cohomology of the complement of the reflection arrangement of a finite Coxeter group W. As a result we complete the verification of a conjecture by Felder and Veselov that gives an explicit basis of the space of W-invariants in this cohomology ring.
J. Matthew Douglass +2 more
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Shi arrangements and low elements in affine Coxeter groups
Canadian Journal of Mathematics, 2023 AbstractGiven an affine Coxeter group W, the corresponding Shi arrangement is a refinement of the corresponding Coxeter hyperplane arrangements that was introduced by Shi to study Kazhdan–Lusztig cells for W. Shi showed that each region of the Shi arrangement contains exactly one element of minimal length in W.
Chapelier-Laget, Nathan +1 more
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Hyperfactord of Shi arrangement Sh(A2) and Sh(A3)
Al-Mustansiriyah Journal of Science, 2022 In this paper, we introduce the region and the faces poset of shi arrangement that J. Y. Shi firstly introduced it. This is an affine arrangement, each of whose hyperplane is parallel to some"hyperplane of Coxeter arrangement"(Braid arrangement), the ...
Alaa A. A. Al-Mujmaey +1 more
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Gallery Posets of Supersolvable Arrangements [PDF]
Discrete Mathematics & Theoretical Computer Science, 2014 We introduce a poset structure on the reduced galleries in a supersolvable arrangement of hyperplanes. In particular, for Coxeter groups of type A or B, we construct a poset of reduced words for the longest element whose Hasse diagram is the graph of ...
Thomas McConville
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The freeness of Ish arrangements [PDF]
Discrete Mathematics & Theoretical Computer Science, 2015 The Ish arrangement was introduced by Armstrong to give a new interpretation of the $q; t$-Catalan numbers of Garsia and Haiman. Armstrong and Rhoades showed that there are some striking similarities between the Shi arrangement and the Ish arrangement ...
Takuro Abe +2 more
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