Combinatorial models for Quasicrystals and Schur-Weyl Duality

Source abstract

Quasicrystals were defined by Cain and Malheiro and Maas-Gariépy to model the decomposition of Schur polynomials into fundamental quasisymmetric functions. We define a new combinatorial model for crystal graphs of type $A_{n-1}$, called parsed content words, for which the decomposition into quasicrystals is particularly evident. We use the model to describe a combinatorial interpretation of Schur-Weyl duality and recover the classical combinatorial proof of the well-known expansion of homogeneous symmetric functions into Schur functions within our framework.