Paths and tableaux descriptions of Jacobi-Trudi determinant associated with quantum affine algebra of type C_n
Quantum Algebra
2007-07-24 v2 Combinatorics
Abstract
We study the Jacobi-Trudi-type determinant which is conjectured to be the q-character of a certain, in many cases irreducible, finite-dimensional representation of the quantum affine algebra of type C_n. Like the D_n case studied by the authors recently, applying the Gessel-Viennot path method with an additional involution and a deformation of paths, we obtain a positive sum expression over a set of tuples of paths, which is naturally translated into the one over a set of tableaux on a skew diagram.
Keywords
Cite
@article{arxiv.math/0604158,
title = {Paths and tableaux descriptions of Jacobi-Trudi determinant associated with quantum affine algebra of type C_n},
author = {Wakako Nakai and Tomoki Nakanishi},
journal= {arXiv preprint arXiv:math/0604158},
year = {2007}
}
Comments
21 pages, 10 figures, the final (journal) version published in SIGMA at http://www.emis.de/journals/SIGMA/