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Paths and Tableaux descriptions of Jacobi-Trudi determinant associated with quantum affine algebra of type Dn

By Wakako Nakai and Tomoki Nakanishi


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 Cn. Like the Dn 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. 1

Year: 2012
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