Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 3 (2007), 078, 20 pages      math.QA/0604158

Paths and Tableaux Descriptions of Jacobi-Trudi Determinant Associated with Quantum Affine Algebra of Type Cn

Wakako Nakai and Tomoki Nakanishi
Graduate School of Mathematics, Nagoya University, Nagoya 464-8602, Japan

Received May 03, 2007, in final form July 04, 2007; Published online July 18, 2007

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 an expression by a positive sum over a set of tuples of paths, which is naturally translated into the one over a set of tableaux on a skew diagram.

Key words: quantum group; q-character; lattice path; Young tableau.

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