Paths and tableaux descriptions of Jacobi-Trudi determinant associated with quantum affine algebra of type C_n
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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 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.
2000 Mathematics Subject Classification: 17B37; 05E15
- Symmetry, Integrability and Geometry: Methods and Applications
Symmetry, Integrability and Geometry: Methods and Applications (3), 78-78, 2007-07-18
Researchers of the Department of Applied Research, Institute of Mathematics of National Academy of Sciences of Ukraine