Fully commutative elements in Coxeter groups and the Temperley-Lieb algebra

In the first​ part of this seminar we will introduce Coxeter groups, fully commutative elements and the Temperley-Lieb algebra, by illustrating some classical examples. In the second part, we will recall a recent construction of a diagrammatic representation of the Temperly-Lieb algebra of affine type C due to Dana Ernst, and we will show that this representation is faithfull in a new combinatorial way.