Geodesic
Paths and tableaux descriptions of Jacobi-Trudi determinant associated with quantum affine algebra of type $D_n$
Journal of Algebraic Combinatorics, Tome 26 (2007) no. 2, pp. 253-290.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: 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 an expression of the determinant by a positive sum over a set of tuples of paths. However, applying 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.
Keywords: keywords quantum group, $q$-character, lattice path, Young tableau 
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     title = {Paths and tableaux descriptions of {Jacobi-Trudi} determinant associated with quantum affine algebra of type $D_n$},
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Nakai, Wakako; Nakanishi, Tomoki. Paths and tableaux descriptions of Jacobi-Trudi determinant associated with quantum affine algebra of type $D_n$. Journal of Algebraic Combinatorics, Tome 26 (2007) no. 2, pp. 253-290. http://geodesic.mathdoc.fr/item/JAC_2007__26_2_a0/