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Symmetry, Integrability and Geometry: Methods and Applications, 2007, Volume 3, 078, 20 pp.
DOI: https://doi.org/10.3842/SIGMA.2007.078 (Mi sigma204) 		 
This article is cited in 11 scientific papers (total in 11 papers)

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

Wakako Nakai, Tomoki Nakanishi

Graduate School of Mathematics, Nagoya University, Nagoya 464-8602, Japan
Full-text PDF (537 kB) Citations (11)
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DOI: https://doi.org/10.3842/SIGMA.2007.078
Abstract: 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.
Keywords: quantum group; $q$-character; lattice path; Young tableau.
Received: May 3, 2007; in final form July 4, 2007; Published online July 18, 2007
Bibliographic databases:
Document Type: Article
MSC: 17B37; 05E15
Language: English
Citation: Wakako Nakai, Tomoki Nakanishi, “Paths and Tableaux Descriptions of Jacobi–Trudi Determinant Associated with Quantum Affine Algebra of Type $C_n$”, SIGMA, 3 (2007), 078, 20 pp.
Citation in format AMSBIB
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\by Wakako Nakai, Tomoki Nakanishi
\paper Paths and Tableaux Descriptions of Jacobi--Trudi Determinant Associated with Quantum Affine Algebra of Type $C_n$
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\vol 3
\papernumber 078
\totalpages 20
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    • This publication is cited in the following 11 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Symmetry, Integrability and Geometry: Methods and Applications
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