Crystal graphs for general linear Lie superalgebras and quasi-symmetric functions

We give a new representation theoretic interpretation of the ring of quasisymmetric functions. This is obtained by showing that the super analogue of the Gessel’s fundamental quasi-symmetric function can be realized as the character of an irreducible crystal for the Lie superalgebra gln|n associated to its non-standard Borel subalgebra with a maximal number of odd isotropic simple roots. We also present an algebraic characterization of these super quasi-symmetric functions.