49 citations · 71 across the 16 of their papers we have counts for
20 papers
Root Systems, Tits Cones and Imaginary Cones of Brink-Howlett Groupoids
Matthew Dyer, Harrison Gimenez
We extend the basic theory of the groupoids introduced by Brink and Howlett in their study of normalizers of parabolic subgroups of Coxeter groups, by studying both their abstract…
A study of intersections of Schubert varieties
M. Dyer, G. Lusztig
We study the local and global intersection cohomology of the intersection of two Schubert varieties in a flag manifold. In this version some new references are added.
Shi arrangements and low elements in Coxeter groups
Matthew Dyer, Christophe Hohlweg, Susanna Fishel +1
Given an arbitrary Coxeter system and a nonnegative integer , the -Shi arrangement of is a subarrangement of the Coxeter hyperplane arrangement of . Th…
The intermediate orders of a Coxeter group
Angela Carnevale, Matthew Dyer, Paolo Sentinelli
We define a class of partial orders on a Coxeter group associated with sets of reflections. In special cases, these lie between the left weak order and the Bruhat order. We prove t…
A characterization of simplicial oriented geometries as groupoids with root systems
Matthew Dyer, Weijia Wang
This paper shows that simplicial oriented geometries can be characterized as groupoids with root systems having certain favorable properties, as conjectured by the first author. Th…
Oriented Matroid Structures From Realized Root Systems
Matthew Dyer, Weijia Wang
This paper investigates the question of uniqueness of the reduced oriented matroid structure arising from root systems of a Coxeter group in real vector spaces. We settle the quest…