Bernard Leclerc

Splitting the Square of a Schur Function into its Symmetric and Antisymmetric Parts

We propose a new combinatorial description of the product of two Schur functions. In the particular case of the square of a Schur function SI, it allows to discriminate in a very natural way between the symmetric and antisymmetric parts of the square. In other words, it describes at the same time the expansion on the basis of Schur functions of the plethysms S2(SI) and Λ2(SI). More generally our combinatorial interpretation of the multiplicities cIJK = SISJ, SKleads to interesting q-analogues cIJK(q) of these multiplicities. The combinatorial objects that we use are domino tableaux, namely tableaux made up of 1 × 2 rectangular boxes filled with integers weakly increasing along the rows and strictly increasing along the columns. Standard domino tableaux have already been considered by many authors [33], [6], [34], [8], [1], but, to the best of our knowledge, the expression of the Littlewood-Richardson coefficients in terms of Yamanouchi domino tableaux is new, as well as the bijection described in Section 7, and the notion of the diagonal class of a domino tableau, defined in Section 8. This construction leads to the definition of a new family of symmetric functions (H-functions), whose relevant properties are summarized in Section 9.

Crystal graphs andq-analogues of weight multiplicities for the root systemA n

AbstractWe give an expression of theq-analogues of the multiplicities of weights in irreduciblen

Curing of aqueous polymeric film coatings: Importance of the coating level and type of plasticizer.

mathfrak{s}mathfrak{l}_{n + 1} - modules

Modelling of drug release from pellets coated with an insoluble polymeric membrane

n in terms of the geometry of the crystal graph attached to correspondingn

Diffusion of a dispersed solute in a polymeric matrix

U_q (mathfrak{s}mathfrak{l}_{n + 1} ) - modules

In situ determination of the diffusion coefficient of a solute in a gel system using a radiotracer

n. As an application, we describe multivariate polynomial analogues of the multiplicities of the zero weight, refining Kostants generalized exponents.