Results 1 to 10 of about 833 (53)

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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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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Dunkl Operators for Complex Reflection Groups [PDF]

, 2001
Dunkl operators for complex reflection groups are defined in this paper. These commuting operators give rise to a parameterized family of deformations of the polynomial De Rham complex. This leads to the study of the polynomial ring as a module over the ‘
C. Dunkl, E. Opdam
semanticscholar   +1 more source

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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Seminormal Representations of Weyl Groups and Iwahori‐Hecke Algebras [PDF]

, 1995
The purpose of this paper is to describe a general procedure for computing analogues of Young's seminormal representations of the symmetric groups. The method is to generalize the Jucys‐Murphy elements in the group algebras of the symmetric groups to ...
Arun Ram
semanticscholar   +1 more source

Commensurability and separability of quasiconvex subgroups [PDF]

, 2006
We show that two uniform lattices of a regular right-angled Fuchsian building are commensurable, provided the chamber is a polygon with at least six edges. We show that in an arbitrary Gromov-hyperbolic regular right-angled building associated to a graph
Frédéric Haglund
semanticscholar   +1 more source

Homological stability for Artin monoids

Proceedings of the London Mathematical Society, Volume 121, Issue 3, Page 537-583, September 2020., 2020
Abstract We prove that certain sequences of Artin monoids containing the braid monoid as a submonoid satisfy homological stability. When the K(π,1) conjecture holds for the associated family of Artin groups, this establishes homological stability for these groups.
Rachael Boyd
wiley   +1 more source

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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Hyperbolic Coxeter groups with Sierpi\'nski carpet boundary [PDF]

, 2015
We give a necessary and sufficient condition for a hyperbolic Coxeter group with planar nerve to have Sierpiński curve as its Gromov boundary. Mathematics Subjest Classification (2010). 20F67; 20F55, 20F65.
Jacek 'Swikatkowski
semanticscholar   +1 more source

The structure of Euclidean Artin groups [PDF]

, 2013
The Coxeter groups that act geometrically on euclidean space have long been classified and presentations for the irreducible ones are encoded in the well-known extended Dynkin diagrams. The corresponding Artin groups are called euclidean Artin groups and,
Jon McCammond
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