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

JOURNAL OF COMBINATORIAL THEORY SERIES A

卷:116

Article

Kwon, Jae-Hoon

关键词: Crystal graphs;    Lie superalgebras;    Quasi-symmetric functions;   

DOI  :  10.1016/j.jcta.2009.03.007

来源: Elsevier

【 摘 要 】

We give a new representation theoretic interpretation of the ring of quasi-symmetric functions. This is obtained by showing that the super analogue of Gessel's fundamental quasi-symmetric function can be realized as the character of a connected crystal for the Lie superalgebra gI(n vertical bar 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. (C) 2009 Elsevier Inc. All rights reserved.

【 授权许可】

Free