Filtration of tensor product of local Weyl modules for $\mathfrak{sl}_{n+1}[t]$
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866909207191617536 |
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| author | Setia, Divya Rani, Shushma Khandai, Tanusree |
| author_facet | Setia, Divya Rani, Shushma Khandai, Tanusree |
| contents | In this paper, we consider the tensor product of local Weyl modules for $\mathfrak{sl}_{n+1}[t]$ whose highest weights are multiples of the first and $n^{th}$ fundamental weights. We determine the graded character of these tensor product modules in terms of the graded character of local Weyl modules and prove that these modules admit a filtration whose successive quotients are either truncated Weyl modules or fusion products of Demazure modules. Furthermore, we establish that the truncated Weyl modules appearing as quotients in the filtration of tensor products of local Weyl modules of $\mathfrak{sl}_3[t]$ are indeed isomorphic to fusion products of irreducible $\mathfrak{sl}_3[t]$-modules which establish the independence of a family of fusion product modules of $\mathfrak{sl}_3[t]$ from the set of its evaluation parameters. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_11944 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Filtration of tensor product of local Weyl modules for $\mathfrak{sl}_{n+1}[t]$ Setia, Divya Rani, Shushma Khandai, Tanusree Representation Theory Rings and Algebras 17B10, 17B35, 17B65, 17B67, 17B70 In this paper, we consider the tensor product of local Weyl modules for $\mathfrak{sl}_{n+1}[t]$ whose highest weights are multiples of the first and $n^{th}$ fundamental weights. We determine the graded character of these tensor product modules in terms of the graded character of local Weyl modules and prove that these modules admit a filtration whose successive quotients are either truncated Weyl modules or fusion products of Demazure modules. Furthermore, we establish that the truncated Weyl modules appearing as quotients in the filtration of tensor products of local Weyl modules of $\mathfrak{sl}_3[t]$ are indeed isomorphic to fusion products of irreducible $\mathfrak{sl}_3[t]$-modules which establish the independence of a family of fusion product modules of $\mathfrak{sl}_3[t]$ from the set of its evaluation parameters. |
| title | Filtration of tensor product of local Weyl modules for $\mathfrak{sl}_{n+1}[t]$ |
| topic | Representation Theory Rings and Algebras 17B10, 17B35, 17B65, 17B67, 17B70 |
| url | https://arxiv.org/abs/2405.11944 |