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Paths and Tableaux Descriptions of Jacobi-Trudi Determinant Associated with Quantum Affine Algebra of Type Cn

Paths and Tableaux Descriptions of Jacobi-Trudi Determinant Associated with Quantum Affine Algebra of Type Cn

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 Cn. Like the Dn case studied by the authors recently, applying the Gessel-Viennot path method with an...

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Main Authors: Nakai, W., Nakanishi, T.
Format: Article
Language:English
Published: Інститут математики НАН України 2007
Series:Symmetry, Integrability and Geometry: Methods and Applications
Online Access:http://dspace.nbuv.gov.ua/handle/123456789/147368
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spelling irk-123456789-1473682019-02-15T01:24:13Z Paths and Tableaux Descriptions of Jacobi-Trudi Determinant Associated with Quantum Affine Algebra of Type Cn Nakai, W. Nakanishi, T. 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 Cn. Like the Dn 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. 2007 Article Paths and Tableaux Descriptions of Jacobi-Trudi Determinant Associated with Quantum Affine Algebra of Type Cn / W. Nakai, T. Nakanishi // Symmetry, Integrability and Geometry: Methods and Applications. — 2007. — Т. 3. — Бібліогр.: 28 назв. — англ. 1815-0659 2000 Mathematics Subject Classification: 17B37; 05E15 http://dspace.nbuv.gov.ua/handle/123456789/147368 en Symmetry, Integrability and Geometry: Methods and Applications Інститут математики НАН України
institution Digital Library of Periodicals of National Academy of Sciences of Ukraine
collection DSpace DC
language English
description 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 Cn. Like the Dn 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.
format Article
author Nakai, W.
Nakanishi, T.
spellingShingle Nakai, W.
Nakanishi, T.
Paths and Tableaux Descriptions of Jacobi-Trudi Determinant Associated with Quantum Affine Algebra of Type Cn
Symmetry, Integrability and Geometry: Methods and Applications
author_facet Nakai, W.
Nakanishi, T.
author_sort Nakai, W.
title Paths and Tableaux Descriptions of Jacobi-Trudi Determinant Associated with Quantum Affine Algebra of Type Cn
title_short Paths and Tableaux Descriptions of Jacobi-Trudi Determinant Associated with Quantum Affine Algebra of Type Cn
title_full Paths and Tableaux Descriptions of Jacobi-Trudi Determinant Associated with Quantum Affine Algebra of Type Cn
title_fullStr Paths and Tableaux Descriptions of Jacobi-Trudi Determinant Associated with Quantum Affine Algebra of Type Cn
title_full_unstemmed Paths and Tableaux Descriptions of Jacobi-Trudi Determinant Associated with Quantum Affine Algebra of Type Cn
title_sort paths and tableaux descriptions of jacobi-trudi determinant associated with quantum affine algebra of type cn
publisher Інститут математики НАН України
publishDate 2007
url http://dspace.nbuv.gov.ua/handle/123456789/147368
citation_txt Paths and Tableaux Descriptions of Jacobi-Trudi Determinant Associated with Quantum Affine Algebra of Type Cn / W. Nakai, T. Nakanishi // Symmetry, Integrability and Geometry: Methods and Applications. — 2007. — Т. 3. — Бібліогр.: 28 назв. — англ.
series Symmetry, Integrability and Geometry: Methods and Applications
work_keys_str_mv AT nakaiw pathsandtableauxdescriptionsofjacobitrudideterminantassociatedwithquantumaffinealgebraoftypecn
AT nakanishit pathsandtableauxdescriptionsofjacobitrudideterminantassociatedwithquantumaffinealgebraoftypecn
first_indexed 2023-05-20T17:27:10Z
last_indexed 2023-05-20T17:27:10Z
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