Results 1 to 10 of about 61 (61)
Equivariant perverse sheaves on Coxeter arrangements and buildings [PDF]
Épijournal de Géométrie Algébrique, 2019 When $W$ is a finite Coxeter group acting by its reflection representation on $E$, we describe the category ${\mathsf{Perv}}_W(E_{\mathbb C}, {\mathcal{H}}_{\mathbb C})$ of $W$-equivariant perverse sheaves on $E_{\mathbb C}$, smooth with respect to the ...
Martin H. Weissman
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Relation spaces of hyperplane arrangements and modules defined by graphs of fiber zonotopes [PDF]
Israel Journal of Mathematics, 2014 We study the exactness of certain combinatorially defined complexes which generalize the Orlik-Solomon algebra of a geometric lattice. The main results pertain to complex reflection arrangements and their restrictions. In particular, we consider the corresponding relation complexes and give a simple proof of the $n$-formality of these hyperplane ...
Finis, T., Lapid, E.
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On the Orlik–Terao ideal and the relation space of a hyperplane arrangement
Advances in Applied Mathematics, 2015 The relation space of a hyperplane arrangement is the vector space of all linear dependencies among the defining forms of the hyperplanes in the arrangement. In this paper, we study the relationship between the relation space and the Orlik--Terao ideal of an arrangement. In particular, we characterize spanning sets of the relation space in terms of the
Dinh Van Le, Fatemeh Mohammadi
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Freeness of hyperplane arrangements and related topics [PDF]
Annales de la Faculté des sciences de Toulouse : Mathématiques, 2014 These are the expanded notes of the lecture by the author in “Arrangements in Pyrénées”, June 2012. We are discussing relations of freeness and splitting problems of vector bundles, several techniques proving freeness of hyperplane arrangements, K. Saito’s theory of primitive derivations for Coxeter arrangements, their application to combinatorial ...
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On a Family of Hyperplane Arrangements Related to the Affine Weyl Groups [PDF]
Journal of Algebraic Combinatorics, 1997 Let \(\Phi\) be an irreducible crystallographic root system in \({\mathbb R}^n\). The hyperplanes defined by \(\alpha(x)=0\) and \(\alpha(x)=1\), where \(\alpha\) ranges over the positive roots of \(\Phi\), form an arrangement \({\mathcal A}={\mathcal A}(\Phi)\). These arrangements were studied by \textit{J.-Y.
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On a conjecture of Athanasiadis related to freeness of a family of hyperplane arrangements [PDF]
Mathematical Research Letters, 2012 6 pages, v2: minor ...
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On a class of diophantine equations related to the numbers of cells in hyperplane arrangements
Journal of Number Theory, 2009 The author studies the diophantine equation \[ {x\choose m}+\dots+{x\choose 1}={y\choose n}+\dots+{y\choose 1} \] in integers \(x\geq m\) and \(y\geq n\), where \(m\) and \(n\) are distinct integers greater than \(1\). The equation can be nicely interpreted geometrically: one asks when the numbers of cells in two simple hyperplane arrangements are ...
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, 2003 In this paper we study a collections of operators $a(k)$ satisfying the "$q_{kl} $-canonical commutation relations" $a(k)a^{+}(l)-q_{kl}a^{+}(l)a(k) =δ_{kl} $ (corresponding for $q_{kl}=q$ to Greenberg (infinite) statistics, for $q=\pm 1$ to classical Bose and Fermi statistics).We show that $n!\times n!$ matrices $A_{n}(\{q_{kl}\})$ of scalar products ...
Meljanac, Stjepan, Svrtan, Dragutin
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A tropical morphism related to the hyperplane arrangement of the complete bipartite graph
, 2004 18 pages, 5 ...
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