Mathematics – Quantum Algebra
Scientific paper
2006-03-07
J. Alg. Combin. 26 (2007) 253-290
Mathematics
Quantum Algebra
38 pages, 24 figures, final version to appear in J. Algebraic Combin
Scientific paper
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.
Nakai Wakako
Nakanishi Tomoki
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