11 papers
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…
On planar algebras arising from hypergroups
R. M. Green
Let be an associative algebra with identity and with trace. We study the family of planar algebras on 1-boxes that arise from in the work of Jones, but with the added assum…
Categories arising from tabular algebras
R. M. Green
We continue the investigation of tabular algebras with trace (a certain class of associative -algebras equipped with distinguished bases) by determining the ex…
Decorated tangles and canonical bases
R. M. Green
We study the combinatorics of fully commutative elements in Coxeter groups of type for any . Using the results, we construct certain canonical bases (i.e., IC bases) f…
Tabular algebras and their asymptotic versions
R. M. Green
We introduce tabular algebras, which are simultaneous generalizations of cellular algebras (in the sense of Graham-Lehrer) and table algebras (in the sense of Arad-Blau). We show t…
Fully commutative Kazhdan-Lusztig cells
R. M. Green, J. Losonczy
We investigate the compatibility of the set of fully commutative elements of a Coxeter group with the various types of Kazhdan-Lusztig cells using a canonical basis for a generaliz…