Results 1 to 10 of about 42 (42)
Symmetry of Narayana Numbers and Rowvacuation of Root Posets
Forum of Mathematics, Sigma, 2021 For a Weyl group W of rank r, the W-Catalan number is the number of antichains of the poset of positive roots, and the W-Narayana numbers refine the W-Catalan number by keeping track of the cardinalities of these antichains.
Colin Defant, Sam Hopkins
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Intersecting principal Bruhat ideals and grades of simple modules [PDF]
, 2022 We prove that the grades of simple modules indexed by boolean permutations, over the incidence algebra of the symmetric group with respect to the Bruhat order, are given by Lusztig's \(\mathbf{a}\)-function. Our arguments are combinatorial, and include a
Tenner, Bridget Eileen +1 more
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Harmonic differential forms for pseudo-reflection groups II. Bi-degree bounds [PDF]
, 2023 This paper studies three results that describe the structure of the super-coinvariant algebra of pseudo-reflection groups over a field of characteristic \(0\).
Wallach, Nolan R., Swanson, Joshua P.
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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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Generalized associahedra via brick polytopes [PDF]
Discrete Mathematics & Theoretical Computer Science, 2012 We generalize the brick polytope of V. Pilaud and F. Santos to spherical subword complexes for finite Coxeter groups. This construction provides polytopal realizations for a certain class of subword complexes containing all cluster complexes of finite ...
Vincent Pilaud, Christian Stump
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Generic Newton points and the Newton poset in Iwahori-double cosets
Forum of Mathematics, Sigma, 2020 We consider the Newton stratification on Iwahori-double cosets in the loop group of a reductive group. We describe a group-theoretic condition on the generic Newton point, called cordiality, under which the Newton poset (that is, the index set for non ...
Elizabeth Milićević, Eva Viehmann
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Fundamental simplices with outer vertices for hyperbolic groups and their group extensions for truncations [PDF]
, 2010 There are investigated supergroups of some hyperbolic space groups with simplicial fundamental domain. If the vertices of these simplices are out of the absolute, we can truncate them by polar planes of the vertices and the new polyhedra are fundamental ...
Milica Stojanovic, Stojanović, Milica
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Commuting involution graphs for [(A)\tilde]n
, 2006 In this article we consider the commuting graphs of involution conjugacy classes in the affine Weyl group A~n. We show that where the graph is connected the diameter is at most 6.
Hart, Sarah, Hart, Sarah B.
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Bender–Knuth Billiards in Coxeter Groups
Forum of Mathematics, SigmaLet $(W,S)$ be a Coxeter system, and write $S=\{s_i:i\in I\}$ , where I is a finite index set. Fix a nonempty convex subset $\mathscr {L}$ of W. If W is of type A, then $\mathscr {L}$ is the set of linear extensions of a poset,
Grant Barkley +4 more
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, 2012 We calculate the growth functions of noncompact 3-dimensional hyperbolic Coxeter groups with 4 and 5 generators.Teichmuller Space and Related Topics : Proceedings of the workshop on Geometry, January 20, 2011, JOSAI UNIVERSITY / edited by Kiyoko ...
小森, 洋平, 梅本, 悠莉子
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