Paths and Tableaux Descriptions of Jacobi-Trudi Determinant Associated with Quantum Affine Algebra of Type $C_n$
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...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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National Academy of Science of Ukraine
2007-07-01
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| Series: | Symmetry, Integrability and Geometry: Methods and Applications |
| Subjects: | |
| Online Access: | http://www.emis.de/journals/SIGMA/2007/078/ |
| _version_ | 1818888646216908800 |
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| author | Wakako Nakai Tomoki Nakanishi |
| author_facet | Wakako Nakai Tomoki Nakanishi |
| author_sort | Wakako Nakai |
| collection | DOAJ |
| 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 $C_n$. 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. |
| first_indexed | 2024-12-19T16:56:26Z |
| format | Article |
| id | doaj.art-c5abcd1d8648455fa799b0b48a37eb3e |
| institution | Directory Open Access Journal |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2024-12-19T16:56:26Z |
| publishDate | 2007-07-01 |
| publisher | National Academy of Science of Ukraine |
| record_format | Article |
| series | Symmetry, Integrability and Geometry: Methods and Applications |
| spelling | doaj.art-c5abcd1d8648455fa799b0b48a37eb3e2022-12-21T20:13:25ZengNational Academy of Science of UkraineSymmetry, Integrability and Geometry: Methods and Applications1815-06592007-07-013078Paths and Tableaux Descriptions of Jacobi-Trudi Determinant Associated with Quantum Affine Algebra of Type $C_n$Wakako NakaiTomoki NakanishiWe 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.http://www.emis.de/journals/SIGMA/2007/078/quantum group$q$-characterlattice pathYoung tableau |
| spellingShingle | Wakako Nakai Tomoki Nakanishi Paths and Tableaux Descriptions of Jacobi-Trudi Determinant Associated with Quantum Affine Algebra of Type $C_n$ Symmetry, Integrability and Geometry: Methods and Applications quantum group $q$-character lattice path Young tableau |
| title | Paths and Tableaux Descriptions of Jacobi-Trudi Determinant Associated with Quantum Affine Algebra of Type $C_n$ |
| title_full | Paths and Tableaux Descriptions of Jacobi-Trudi Determinant Associated with Quantum Affine Algebra of Type $C_n$ |
| title_fullStr | Paths and Tableaux Descriptions of Jacobi-Trudi Determinant Associated with Quantum Affine Algebra of Type $C_n$ |
| title_full_unstemmed | Paths and Tableaux Descriptions of Jacobi-Trudi Determinant Associated with Quantum Affine Algebra of Type $C_n$ |
| title_short | Paths and Tableaux Descriptions of Jacobi-Trudi Determinant Associated with Quantum Affine Algebra of Type $C_n$ |
| title_sort | paths and tableaux descriptions of jacobi trudi determinant associated with quantum affine algebra of type c n |
| topic | quantum group $q$-character lattice path Young tableau |
| url | http://www.emis.de/journals/SIGMA/2007/078/ |
| work_keys_str_mv | AT wakakonakai pathsandtableauxdescriptionsofjacobitrudideterminantassociatedwithquantumaffinealgebraoftypecn AT tomokinakanishi pathsandtableauxdescriptionsofjacobitrudideterminantassociatedwithquantumaffinealgebraoftypecn |