Algèbre de Temperley–Lieb de type B

We give a dual presentation, in the sense of the dual presentation of Artin groups, of the Temperley–Lieb algebra of type B. In particular, we obtain a basis of this algebra by considering the homomorphic images of the simple elements of the dual monoid. This algebra is the largest quotient of the Hecke algebra whose irreducible representations are parametrized by pairs of Young diagrams with at most one column in each component. To cite this article: C. Vincenti, C. R. Acad. Sci. Paris, Ser. I 342 (2006).