16 citations · 30 across the 18 of their papers we have counts for
7 papers · 1 filter
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…
A proof of Lusztig's conjectures for affine type with arbitrary parameters
J. Guilhot, J. Parkinson
We prove Lusztig's conjectures -- for the affine Weyl group of type for all choices of parameters. Our approach to compute Lusztig's …
A classification of commutative parabolic Hecke algebras
Peter Abramenko, James Parkinson, Hendrik Van Maldeghem
Let be a Coxeter system with such that the parabolic subgroup is finite. Associated to this data there is a \textit{Hecke algebra} $\scH$ and a \textit…
On calibrated representations and the Plancherel Theorem for affine Hecke algebras
James Parkinson
This paper has two main purposes. Firstly we generalise Ram's explicit construction of calibrated representations of the affine Hecke algebra to the multi-parameter case (including…
Alcove walks, buildings, symmetric functions and representations
James Parkinson, Arun Ram
For a complex simple Lie algebra, the dimension of the weight space of a finite dimensional representation of highest weight is the same as the number of Littelman…
Combinatorics in affine flag varieties
James Parkinson, Arun Ram, Christoph Schwer
The Littelmann path moel gives a realization of the crystals of integrable representations of symmetrizable Kac-Moody Lie algebras. Recent work of Gaussent-Littelmann and others ha…
Buildings and Hecke algebras
James Parkinson
This paper investigates the connections between buildings and Hecke algebras through the combinatorial study of two algebras spanned by averaging operators on buildings. As a conse…