Conférencière: Elisa Sasso (université de Bologne, Italie)

The Temperley--Lieb algebra is a classical mathematical object studied in algebra, combinatorics, statistical mechanics and mathematical physics, introduced by Temperley and Lieb in 1971. For any Coxeter system, it is possible to define the so-called generalized Temperley—Lieb algebras as quotients of the associated Hecke algebras. Moreover, beginning with the work of Kauffman and Penrose, it was shown that most Temperley--Lieb algebras can be realized as diagram algebras, which are associative algebras with a basis given by certain diagrams on the plane.In this talk, I will introduce a diagrammatic representation for the Temperley--Lieb algebra of type affine D, obtained using particular decorated diagrams. I will also describe some of the combinatorial strategies used to prove the faithfulness of this representation.