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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2411.00675 |
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| _version_ | 1866916464699637760 |
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| author | Metzaki, Maria |
| author_facet | Metzaki, Maria |
| contents | Consider partitions of the form $λ=(a,1^b)$ and $μ=(a+1,b-1)$,\\ where $a+1>b-1$. In this paper, we determine the extension groups $\mathrm{Ext}_A^2(K_λF,K_μF)$, where $F$ is a free $\mathbb{Z}-$module of finite rank $n$, $K_λF$ and $K_μF$ are the Weyl modules of the general linear group $GL_n(\mathbb{Z})$ corresponding to $λ$ and $μ$, respectively, $A=S_\mathbb{Z}(n,r)$ is the integral Schur algebra and $r=a+b$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_00675 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On integral $\mathrm{Ext^2}$ between certain Weyl modules of $\mathrm{GLn}$ Metzaki, Maria Representation Theory 20G05 Consider partitions of the form $λ=(a,1^b)$ and $μ=(a+1,b-1)$,\\ where $a+1>b-1$. In this paper, we determine the extension groups $\mathrm{Ext}_A^2(K_λF,K_μF)$, where $F$ is a free $\mathbb{Z}-$module of finite rank $n$, $K_λF$ and $K_μF$ are the Weyl modules of the general linear group $GL_n(\mathbb{Z})$ corresponding to $λ$ and $μ$, respectively, $A=S_\mathbb{Z}(n,r)$ is the integral Schur algebra and $r=a+b$. |
| title | On integral $\mathrm{Ext^2}$ between certain Weyl modules of $\mathrm{GLn}$ |
| topic | Representation Theory 20G05 |
| url | https://arxiv.org/abs/2411.00675 |