D_n型量子仿射代数的Jacobi-Trudi行列式的路与表描述
Paths and tableaux descriptions of Jacobi-Trudi determinant associated with quantum affine algebra of type D_n
摘要：
本文研究了D_n型量子仿射代数的有限维表示的Jacobi-Trudi型行列式，它被证明是D_n型量子仿射代数的某种有限维表示的q-特征标。与A_n和B_n情形不同，Gessel-Viennot路径方法的简单应用并不产生路径元组集合上行列式的正和表达式。然而，应用一个额外的对合和变形的路径，我们得到了一个正和表达式的一组元组的路径，这是自然地转换成一组的tableaux上的斜图。
英文摘要：
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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