Generalized Temperley–Lieb Diagrams and the Mathas–Lusztig Involution

This page explores the Mathas–Lusztig involution on Fully Commutative elements of Coxeter systems. In particular, it realizes such elements as diagrams: elements of Generalized Temperley–Lieb algebras. On the page corresponding to each Coxeter system, the "canonical diagrams" associated to each FC-element pair are displayed side-by-side. Each page includes filtering functionality, and the option to display only pairs of elements that actually differ under the involution.

This data was collected with the help and direction of Tianyuan Xu, as part of an REU at University of Colorado Boulder. For more information, see

• The REU page
• Our Sage fork containing the code used to work with these diagrams and generate the data found on this page