Paths and tableaux descriptions of Jacobi-Trudi determinant associated with quantum affine algebra of type D n

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 an expression of the determinant by a positive sum over a set of tuples of paths. However, applying an additional involution and a deformation of paths, we obtain an expression by a positive sum over a set of tuples of paths, which is naturally translated into the one over a set of tableaux on a skew diagram.