16 citations · 30 across the 18 of their papers we have counts for
24 papers
Automorphisms and opposition in spherical buildings of classical type
James Parkinson, Hendrik Van Maldeghem
An automorphism of a spherical building is called domestic if it maps no chamber to an opposite chamber. In this paper we classify domestic automorphisms of spherical buildings of…
On -folded alcove paths and combinatorial representations of affine Hecke algebras
Jérémie Guilhot, Eloise Little, James Parkinson
We introduce the combinatorial model of -folded alcove paths in an affine Weyl group and construct representations of affine Hecke algebras using this model. We study boundednes…
Automorphisms and opposition in spherical buildings of exceptional type, II: Moufang hexagons
James Parkinson, Hendrik Van Maldeghem
We classify the automorphisms of a Moufang hexagon mapping no chamber to an opposite chamber (such automorphisms are called domestic). This forms part of a larger program to classi…
Cone Types, Automata, and Regular Partitions in Coxeter Groups
James Parkinson, Yeeka Yau
In this article we introduce the notion of a \textit{regular partition} of a Coxeter group. We develop the theory of these partitions, and show that the class of regular partitions…
Automorphisms and opposition in spherical buildings of exceptional type, I
James Parkinson, Hendrik Van Maldeghem
To each automorphism of a spherical building there is naturally associated an "opposition diagram", which encodes the types of the simplices of the building that are mapped onto op…
Patterns in sets of positive density in trees and affine buildings
M. Björklund, A. Fish, J. Parkinson
We prove an analogue for homogeneous trees and certain affine buildings of a result of Bourgain on pinned distances in sets of positive density in Euclidean spaces. Furthermore, we…