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

Wakako Nakai·Tomoki Nakanishi
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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.

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Wakako Nakai, Tomoki Nakanishi. 2006-03-07. Paths and tableaux descriptions of Jacobi-Trudi determinant associated with quantum affine algebra of type D_n. https://arxiv.org/abs/math/0603160

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