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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| Language: | English |
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Cambridge University Press
2025-01-01
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| Series: | Forum of Mathematics, Sigma |
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| Online Access: | https://www.cambridge.org/core/product/identifier/S2050509425000179/type/journal_article |
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| author | You-Hung Hsu |
| author_facet | You-Hung Hsu |
| author_sort | You-Hung Hsu |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-43d02193d2554499a4d7f4f96dd8bb08 |
| institution | OA Journals |
| issn | 2050-5094 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | Cambridge University Press |
| record_format | Article |
| series | Forum of Mathematics, Sigma |
| spelling | doaj-art-43d02193d2554499a4d7f4f96dd8bb082025-08-20T02:26:31ZengCambridge University PressForum of Mathematics, Sigma2050-50942025-01-011310.1017/fms.2025.17A categorical action of the shifted $0$ -affine algebraYou-Hung Hsu0https://orcid.org/0000-0001-9073-5323Institute of Mathematics, Academia Sinica, No. 1, Sec. 4, Roosevelt Road, Da-an, Taipei, 106319, TaiwanWe 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.https://www.cambridge.org/core/product/identifier/S2050509425000179/type/journal_article14M1518G8018N2520C0820G42 |
| spellingShingle | You-Hung Hsu A categorical action of the shifted $0$ -affine algebra Forum of Mathematics, Sigma 14M15 18G80 18N25 20C08 20G42 |
| title | A categorical action of the shifted $0$ -affine algebra |
| title_full | A categorical action of the shifted $0$ -affine algebra |
| title_fullStr | A categorical action of the shifted $0$ -affine algebra |
| title_full_unstemmed | A categorical action of the shifted $0$ -affine algebra |
| title_short | A categorical action of the shifted $0$ -affine algebra |
| title_sort | categorical action of the shifted 0 affine algebra |
| topic | 14M15 18G80 18N25 20C08 20G42 |
| url | https://www.cambridge.org/core/product/identifier/S2050509425000179/type/journal_article |
| work_keys_str_mv | AT youhunghsu acategoricalactionoftheshifted0affinealgebra AT youhunghsu categoricalactionoftheshifted0affinealgebra |