Sadek Alharbat (University of Leeds) – "Thi" good Bijection Between FC Elements and Non-Crossing Diagrams: CataLand

I shall explain Theorem (127) which determines the unique bijection BETWEEN the monomial basis called $(A_n)$- FC elements  AND the set of non-crossing diagrams of $n+1$ strings OF  our well-known Temperley-Lieb algebra, that respects the  diagrammatic multiplication by concatenation along with the two algorithms implementing this bijection and its inverse, in other terms : "Drawing" a basis element into a diagram and "writing" a diagram as member in the monomial basis.

Naturally  we shall find ourselves in CataLand, so I will try to give -as much as our time allows me- some consequences and open problems coming from the above holly marriage, that is to explain why did I commit this work (other than the obvious reasons). The talk is pretty simple & basically addressed to our Ph.D students, accessible to Master students and in which there is an introduction to my talk next week.