In this talk, we present our results concerning Temperley–Lieb diagram algebras of types A and B, which have a basis indexed by the fully commutative elements in Coxeter groups of types A and B, respectively. In particular, we present a non-recursive method for enumerating the number of generators occurring in the fully commutative element that indexes a given diagram. One consequence of our results is a classification of the diagrams of the Temperley–Lieb algebras of types A and B indexed by cyclically fully commutative elements.
This talk was given by my undergraduate research students Sarah Otis and Leal Rivanis (Plymouth State University) on April 17, 2010 at the 2010 Hudson River Undergraduate Mathematics Conference at Keene State College.