Graded Character Formula for Fusion Products of Irreducible Modules and Littlewood-Richardson Coefficients in Type $A_2$
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866911773974593536 |
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| author | Khandai, Tanusree Rani, Shushma |
| author_facet | Khandai, Tanusree Rani, Shushma |
| contents | We investigate a specific class of CV modules for $\mathfrak{sl}_3$ and establish an exact sequence for these modules. Utilizing dimension arguments, we demonstrate that this module is isomorphic to the fusion product of irreducible modules, thereby offering a new proof of the conjecture regarding the independence of fusion products from parameters. By analyzing the filtration of the kernel within the exact sequence, we derive the graded character formula for fusion product modules. Moreover, we leverage the graded character to deduce the algebraic characterization of the Littlewood-Richardson (LR) coefficients and present an alternative proof of the saturation theorem in type $A_2$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2303_03337 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Graded Character Formula for Fusion Products of Irreducible Modules and Littlewood-Richardson Coefficients in Type $A_2$ Khandai, Tanusree Rani, Shushma Representation Theory Rings and Algebras 17B10, 52B20, 17B67, 05E10 We investigate a specific class of CV modules for $\mathfrak{sl}_3$ and establish an exact sequence for these modules. Utilizing dimension arguments, we demonstrate that this module is isomorphic to the fusion product of irreducible modules, thereby offering a new proof of the conjecture regarding the independence of fusion products from parameters. By analyzing the filtration of the kernel within the exact sequence, we derive the graded character formula for fusion product modules. Moreover, we leverage the graded character to deduce the algebraic characterization of the Littlewood-Richardson (LR) coefficients and present an alternative proof of the saturation theorem in type $A_2$. |
| title | Graded Character Formula for Fusion Products of Irreducible Modules and Littlewood-Richardson Coefficients in Type $A_2$ |
| topic | Representation Theory Rings and Algebras 17B10, 52B20, 17B67, 05E10 |
| url | https://arxiv.org/abs/2303.03337 |