Paths, tableaux and q-characters of quantum affine algebras: the Cn case

For the quantum affine algebra Uq(g-circumflex) with g of classical type, let χλ/μ,a be the Jacobi-Trudi-type determinant for the generating series of the (supposed) q-characters of the fundamental representations. We conjecture that χλ/μ,a is the q-character of a certain finite-dimensional representation of Uq(g-circumflex). We study the tableaux description of χλ/μ,a using the path method due to Gessel-Viennot. It immediately reproduces the tableau rule by Bazhanov-Reshetikhin for An and by Kuniba-Ohta-Suzuki for Bn. For Cn, we derive the explicit tableau rule for skew diagrams λ/μ of three rows and of two columns