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

Abstract

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.

DOI: 10.1016/j.jcta.2009.03.007

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@article{Kwon2009CrystalGF, title={Crystal graphs for general linear Lie superalgebras and quasi-symmetric functions}, author={Jae-Hoon Kwon}, journal={J. Comb. Theory, Ser. A}, year={2009}, volume={116}, pages={1199-1218} }