The Koszul complex and a certain induced module for a quantum group
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arXiv
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| Format: | Preprint |
| Published: |
2022
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| _version_ | 1866917561554173952 |
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| author | Tanisaki, Toshiyuki |
| author_facet | Tanisaki, Toshiyuki |
| contents | We give a description of a certain induced module for a quantum group of type $A$. Together with our previous results this gives a proof of Lusztig's conjectural multiplicity formula for non-restricted modules over the De Concini-Kac type quantized enveloping algebra of type $A_n$ at the $\ell$-th root of unity, where $\ell$ is an odd integer satisfying $(\ell,n+1)=1$ and $\ell> n+1$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2212_12625 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | The Koszul complex and a certain induced module for a quantum group Tanisaki, Toshiyuki Representation Theory Quantum Algebra 20G42, 17B37 We give a description of a certain induced module for a quantum group of type $A$. Together with our previous results this gives a proof of Lusztig's conjectural multiplicity formula for non-restricted modules over the De Concini-Kac type quantized enveloping algebra of type $A_n$ at the $\ell$-th root of unity, where $\ell$ is an odd integer satisfying $(\ell,n+1)=1$ and $\ell> n+1$. |
| title | The Koszul complex and a certain induced module for a quantum group |
| topic | Representation Theory Quantum Algebra 20G42, 17B37 |
| url | https://arxiv.org/abs/2212.12625 |