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arXiv · 0710.0253

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

Jae-Hoon Kwon
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Abstract

We give a new representation theoretic interpretation of the ring of quasi-symmetric 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 $\frak{gl}_{n|n}$ 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.

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BibTeXRIS

Jae-Hoon Kwon. 2007-10-01. Crystal graphs for general linear Lie superalgebras and quasi-symmetric functions. https://arxiv.org/abs/0710.0253

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