A categorical action of the shifted $0$ -affine algebra
We introduce a new algebra $\mathcal {U}=\dot {\mathrm {\mathbf{U}}}_{0,N}(L\mathfrak {sl}_n)$ called the shifted $0$ -affine algebra, which emerges naturally from studying coherent sheaves on n-step partial flag varieties through natural correspondences. This algebra $\mathcal {U}$...
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| Main Author: | |
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| Format: | Article |
| Language: | English |
| Published: |
Cambridge University Press
2025-01-01
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| Series: | Forum of Mathematics, Sigma |
| Subjects: | |
| Online Access: | https://www.cambridge.org/core/product/identifier/S2050509425000179/type/journal_article |
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| Summary: | We introduce a new algebra
$\mathcal {U}=\dot {\mathrm {\mathbf{U}}}_{0,N}(L\mathfrak {sl}_n)$
called the shifted
$0$
-affine algebra, which emerges naturally from studying coherent sheaves on n-step partial flag varieties through natural correspondences. This algebra
$\mathcal {U}$
has a similar presentation to the shifted quantum affine algebra defined by Finkelberg-Tsymbaliuk. Then, we construct a categorical
$\mathcal {U}$
-action on a certain 2-category arising from derived categories of coherent sheaves on n-step partial flag varieties. As an application, we construct a categorical action of the affine
$0$
-Hecke algebra on the bounded derived category of coherent sheaves on the full flag variety. |
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| ISSN: | 2050-5094 |