Resumen de Adjacency of Young tableaux and the Springer fibers

N. G. J. Pagnon, Nicolas Ressayre

• We connect different results about irreducible components of the Springer fibers of type A. Firstly, we show a relation between the Spaltenstein partition of the fibers and a total order on the set of standard Young tableaux. Next, using a result of Steinberg, we connect a work of the first author to the Robinson¿Schensted map. We also perform the Spaltenstein study of the relative position of the Springer fibers and -fibrations of the flag manifold. This leads us to consider the adjacency relation on the set of standard Young tableaux and to define oriented and labeled graphs with the standard Young tableaux as vertices. Using this adjacency relation, we describe some smooth irreducible components of the Springer fibers. Finally, we show that these graphs can be identified with some full subgraphs of the Bruhat graph.