Results 1 to 10 of about 756 (27)

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

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
doaj   +1 more source

Commuting involution graphs for [(A)\tilde]n [PDF]

, 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
core   +1 more source

A note on non-reduced reflection factorizations of Coxeter elements [PDF]

, 2019
We extend a result of Lewis and Reiner from finite Coxeter groups to all Coxeter groups by showing that two reflection factorizations of a Coxeter element lie in the same Hurwitz orbit if and only if they share the same multiset of conjugacy classes ...
Wegener, Patrick, Yahiatene, Sophiane
core   +3 more sources

A Limit Relation for Dunkl-Bessel Functions of Type A and B [PDF]

, 2008
We prove a limit relation for the Dunkl-Bessel function of type $B_N$ with multiplicity parameters $k_1$ on the roots $\pm e_i$ and $k_2$ on $\pm e_i\pm e_j$ where $k_1$ tends to infinity and the arguments are suitably scaled.
Rösler, Margit, Voit, Michael
core   +4 more sources

Signature, positive Hopf plumbing and the Coxeter transformation [PDF]

, 2016
By a theorem of A'Campo, the eigenvalues of certain Coxeter transformations are positive real or lie on the unit circle. By optimally bounding the signature of tree-like positive Hopf plumbings from below by the genus, we prove that at least two thirds ...
Liechti, Livio
core   +2 more sources

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
doaj   +1 more source