|Résumé||In 1995, Carré and Leclerc studied a bijection due to Stanton and White between domino tableaux and pairs of Young tableaux. They gave an easier description of this bijection that highlights the role of the diagonals of tableaux. This allows them to extend the plactic monoid of Lascoux and Schützenberger to dominoes, hence, define the super plactic monoid. They show that each class of the super plactic monoid is represented by a unique domino tableau, and propose a new combinatorial description of the product of two Schur functions using domino tableaux, which gives a new expression of the Littlewood-Richardson rule coefficients in terms of domino tableaux.
In a recent work, we defined new combinatorial objects called the shifted domino tableaux, these objects can be seen as a shifted analog of domino tableaux or as an extension of shifted Young tableaux. The purpose of this extension is to develop a theory of shifted domino tableaux parallel to the theory of domino tableaux and shed lights on the combinatorial properties of Q-Schur and P-Schur functions. In this talk I will introduce the shifted domino tableaux, present a bijection between shifted domino tableaux and pairs of shifted Young tableaux, and discuss some results. |