Results 1 to 10 of about 11 (11)

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
doaj   +1 more source

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
doaj   +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
doaj   +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
doaj   +1 more source

Bender–Knuth Billiards in Coxeter Groups

Forum of Mathematics, Sigma
Let $(W,S)$ 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, Colin Defant, Eliot Hodges, Noah Kravitz, Mitchell Lee   +4 more
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Orthogonal roots, Macdonald representations, and quasiparabolic sets

Forum of Mathematics, Sigma
Let W be a simply laced Weyl group of finite type and rank n. If W has type $E_7$ , $E_8$ or $D_n$ for n even, then the root system of W has subsystems of type $nA_1$ .
R. M. Green, Tianyuan Xu
doaj   +1 more source

Affine Bruhat order and Demazure products

Forum of Mathematics, Sigma
We give new descriptions of the Bruhat order and Demazure products of affine Weyl groups in terms of the weight function of the quantum Bruhat graph.
Felix Schremmer
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Cusp Density and Commensurability of Non-arithmetic Hyperbolic Coxeter Orbifolds. [PDF]

Discrete Comput Geom, 2023
Dotti E, Drewitz ST, Kellerhals R.
europepmc   +1 more source

Symmetric Jacobians

Open Mathematics, 2014
Bondt Michiel
doaj   +1 more source

Subword Complexes and Kalai's Conjecture on Reconstruction of Spheres. [PDF]

Discrete Comput Geom
Ceballos C, Doolittle J.
europepmc   +1 more source