Representation Theory of $0$-Schur Algebras and Related Categories
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866909907592151040 |
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| author | Jung, Woo-Seok Oh, Young-Tak |
| author_facet | Jung, Woo-Seok Oh, Young-Tak |
| contents | Jensen, Su, and Yang described the projective indecomposable modules of the $0$-Schur algebra $\mathbf{S}_0(n,r)$ using its geometric realization. In this paper, the simple modules of $\mathbf{S}_0(n,r)$ are identified by computing the tops of the projective indecomposable modules. Furthermore, functorial relations among the module categories $\mathbf{H}_r(0)$\textsf{-mod}, $\mathbf{S}_0(n,r)$\textsf{-mod}, and $U_0(\mathfrak{gl}_n)$\textsf{-mod} are examined, where $\mathbf{H}_r(0)$ denotes the $0$-Hecke algebra and $U_0(\mathfrak{gl}_n)$ denotes the degenerate quantum group. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_26194 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Representation Theory of $0$-Schur Algebras and Related Categories Jung, Woo-Seok Oh, Young-Tak Representation Theory Combinatorics 20G43, 20C08, 20G42, 20C25 Jensen, Su, and Yang described the projective indecomposable modules of the $0$-Schur algebra $\mathbf{S}_0(n,r)$ using its geometric realization. In this paper, the simple modules of $\mathbf{S}_0(n,r)$ are identified by computing the tops of the projective indecomposable modules. Furthermore, functorial relations among the module categories $\mathbf{H}_r(0)$\textsf{-mod}, $\mathbf{S}_0(n,r)$\textsf{-mod}, and $U_0(\mathfrak{gl}_n)$\textsf{-mod} are examined, where $\mathbf{H}_r(0)$ denotes the $0$-Hecke algebra and $U_0(\mathfrak{gl}_n)$ denotes the degenerate quantum group. |
| title | Representation Theory of $0$-Schur Algebras and Related Categories |
| topic | Representation Theory Combinatorics 20G43, 20C08, 20G42, 20C25 |
| url | https://arxiv.org/abs/2509.26194 |