Paths and Tableaux Descriptions of Jacobi–Trudi Determinant Associated with Quantum Affine Algebra of Type $C_n$

Wakako Nakai ; Tomoki Nakanishi

Symmetry, integrability and geometry: methods and applications, Tome 3 (2007)

Résumé

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 $C_n$. Like the $D_n$ 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 apositive sum over a set of tuples of paths, which is naturally translated into the one over a set of tableaux on a skew diagram.

Détail

Keywords: quantum group; $q$-character; lattice path; Young tableau.

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