Paths and tableaux descriptions of Jacobi-Trudi determinant associated with quantum affine algebra of type D_n
Quantum Algebra
2011-01-28 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 D_n. Unlike the A_n and B_n cases, a simple application of the Gessel-Viennot path method does not yield a positive sum expression of the determinant over a set of tuples of paths. However, applying 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/0603160,
title = {Paths and tableaux descriptions of Jacobi-Trudi determinant associated with quantum affine algebra of type D_n},
author = {Wakako Nakai and Tomoki Nakanishi},
journal= {arXiv preprint arXiv:math/0603160},
year = {2011}
}
Comments
38 pages, 24 figures, final version to appear in J. Algebraic Combin