$0$-affine quantum groups as K-theoretic Hall algebras
Fuente:
arXiv
Salvato in:
| Autore principale: | |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2025
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866915662405828608 |
|---|---|
| author | Hsu, You-Hung |
| author_facet | Hsu, You-Hung |
| contents | In this note, we show that the positive part of Arkhipov-Mazin's $0$-affine quantum group can be realized as the K-theoretic Hall algebra of the type $A$ Dynkin quiver. We then construct a categorical action of this positive part and demonstrate that such an action induces semiorthogonal decompositions on the corresponding weight categories. As a main example, we study the bounded derived category of coherent sheaves on $n$-step partial flag varieties. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_08272 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | $0$-affine quantum groups as K-theoretic Hall algebras Hsu, You-Hung Representation Theory Primary 17B37, 19L47, 20G42 : Secondary 14F08, 18G80 In this note, we show that the positive part of Arkhipov-Mazin's $0$-affine quantum group can be realized as the K-theoretic Hall algebra of the type $A$ Dynkin quiver. We then construct a categorical action of this positive part and demonstrate that such an action induces semiorthogonal decompositions on the corresponding weight categories. As a main example, we study the bounded derived category of coherent sheaves on $n$-step partial flag varieties. |
| title | $0$-affine quantum groups as K-theoretic Hall algebras |
| topic | Representation Theory Primary 17B37, 19L47, 20G42 : Secondary 14F08, 18G80 |
| url | https://arxiv.org/abs/2512.08272 |