58 citations · 80 across the 18 of their papers we have counts for
18 papers
On Representations of Affine Temperley--Lieb Algebras
R. M. Green
We study the finite-dimensional simple modules, over an algebraically closed field, of the affine Temperley--Lieb algebra corresponding to the affine Weyl group of type . These…
Kazhdan--Lusztig cells of -value 2 in -finite Coxeter systems
R. M. Green, Tianyuan Xu
A Coxeter group is said to be \emph{-finite} if it has finitely many elements of -value 2 in the sense of Lusztig. In this paper, we give explicit combin…
Classification of Coxeter groups with finitely many elements of -value 2
R. M. Green, Tianyuan Xu
We consider Lusztig's -function on Coxeter groups (in the equal parameter case) and classify all Coxeter groups with finitely many elements of -value 2 in t…
Leading coefficients of Kazhdan--Lusztig polynomials and fully commutative elements
R. M. Green
Let be a Coxeter group of type . We show that the leading coefficient, , of the Kazhdan--Lusztig polynomial is always equal to 0 or 1 i…
Generalized Jones traces and Kazhdan--Lusztig bases
R. M. Green
We develop some applications of certain algebraic and combinatorial conditions on the elements of Coxeter groups, such as elementary proofs of the positivity of certain structure c…
On rank functions for heaps
R. M. Green
Motivated by work of Stembridge, we study rank functions for Viennot's heaps of pieces. We produce a simple and sufficient criterion for a heap to be a ranked poset and apply the r…