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 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.

38 pages, 24 figures, final version to appear in J. Algebraic Combin

References in corpus (3)

• On minimal affinizations of representations of quantum groups
• Paths, tableaux, and q-characters of quantum affine algebras: the C_n case
• Difference L operators and a Casorati determinant solution to the T-system for twisted quantum affine algebras

Cited by in corpus (1)

• Jacobi-Trudi determinants and characters of minimal affinizations