Results 111 to 120 of about 177 (130)
Coxeter and crystallographic arrangements are inductively free
Advances in Mathematics, 2012 22 ...
Michael Cuntz, Mohamed Barakat
exaly +4 more sources
Counting chambers in restricted Coxeter arrangements
Archiv Der Mathematik, 2019 11 ...
Gerhard Roehrle, Röhrle Gerhard
exaly +4 more sources
The primitive derivation and freeness of multi-Coxeter arrangements
Proceedings of the Japan Academy Series A: Mathematical Sciences, 2002 We will prove the freeness of multi-Coxeter arrangements by constructing a basis of the module of vector fields which contact to each reflecting hyperplanes with some multiplicities using K. Saito's theory of primitive derivation.
Masahiko Yoshinaga
exaly +5 more sources
Equivariant multiplicities of Coxeter arrangements and invariant bases
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
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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
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Modules of Differential Operators of Order 2 on Coxeter Arrangements [PDF]
Algebras and Representation Theory, 2013 We prove that the modules of differential operators of order 2 on the classical Coxeter arrangements are free by exhibiting bases. For this purpose, we use Cauchy-Sylvester's theorem on compound determinants and Saito-Holm's criterion. In the case type $A$, we apply Cauchy-Sylvester's theorem on compound determinants to Vandermond determinant. By using
exaly +4 more sources
Some of the next articles are maybe not open access.
Coxeter Arrangements and Solomon's Descent Algebra
2011Oberwolfach Preprints;2011 ...
Douglass, J. Matthew +2 more
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On the Invariants of the Cohomology of Complements of Coxeter Arrangements
2018We 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.
Douglass, J. Matthew +2 more
openaire +1 more source
Bijection and Enumeration of Regions in Certain Coxeter Arrangements
2023An n-dimensional real hyperplane arrangement is a finite collection of affine hyperplanesin R^n.
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