Toward AGT for Parabolic Sheaves
<jats:title>Abstract</jats:title> <jats:p>We construct explicit elements $W_{ij}^k$ in (a completion of) the shifted quantum toroidal algebra of type $A$ and show that these elements act by 0 on the $K$-theory of moduli spaces of parabolic sheaves. We expect that th...
| Main Author: | |
|---|---|
| Other Authors: | |
| Format: | Article |
| Language: | English |
| Published: |
Oxford University Press (OUP)
2022
|
| Online Access: | https://hdl.handle.net/1721.1/145815 |
| _version_ | 1826189654962995200 |
|---|---|
| author | Neguţ, Andrei |
| author2 | Massachusetts Institute of Technology. Department of Mathematics |
| author_facet | Massachusetts Institute of Technology. Department of Mathematics Neguţ, Andrei |
| author_sort | Neguţ, Andrei |
| collection | MIT |
| description | <jats:title>Abstract</jats:title>
<jats:p>We construct explicit elements $W_{ij}^k$ in (a completion of) the shifted quantum toroidal algebra of type $A$ and show that these elements act by 0 on the $K$-theory of moduli spaces of parabolic sheaves. We expect that the quotient of the shifted quantum toroidal algebra by the ideal generated by the elements $W_{ij}^k$ will be related to $q$-deformed $W$-algebras of type $A$ for arbitrary nilpotent, which would imply a $q$-deformed version of the Alday-Gaiotto-Tachikawa (AGT) correspondence between gauge theory with surface operators and conformal field theory.</jats:p> |
| first_indexed | 2024-09-23T08:19:22Z |
| format | Article |
| id | mit-1721.1/145815 |
| institution | Massachusetts Institute of Technology |
| language | English |
| last_indexed | 2024-09-23T08:19:22Z |
| publishDate | 2022 |
| publisher | Oxford University Press (OUP) |
| record_format | dspace |
| spelling | mit-1721.1/1458152022-10-14T03:47:03Z Toward AGT for Parabolic Sheaves Neguţ, Andrei Massachusetts Institute of Technology. Department of Mathematics <jats:title>Abstract</jats:title> <jats:p>We construct explicit elements $W_{ij}^k$ in (a completion of) the shifted quantum toroidal algebra of type $A$ and show that these elements act by 0 on the $K$-theory of moduli spaces of parabolic sheaves. We expect that the quotient of the shifted quantum toroidal algebra by the ideal generated by the elements $W_{ij}^k$ will be related to $q$-deformed $W$-algebras of type $A$ for arbitrary nilpotent, which would imply a $q$-deformed version of the Alday-Gaiotto-Tachikawa (AGT) correspondence between gauge theory with surface operators and conformal field theory.</jats:p> 2022-10-13T13:37:44Z 2022-10-13T13:37:44Z 2020 2022-10-13T13:33:01Z Article http://purl.org/eprint/type/JournalArticle https://hdl.handle.net/1721.1/145815 Neguţ, Andrei. 2020. "Toward AGT for Parabolic Sheaves." International Mathematics Research Notices, 2022 (9). en 10.1093/IMRN/RNAA308 International Mathematics Research Notices Creative Commons Attribution-Noncommercial-Share Alike http://creativecommons.org/licenses/by-nc-sa/4.0/ application/pdf Oxford University Press (OUP) arXiv |
| spellingShingle | Neguţ, Andrei Toward AGT for Parabolic Sheaves |
| title | Toward AGT for Parabolic Sheaves |
| title_full | Toward AGT for Parabolic Sheaves |
| title_fullStr | Toward AGT for Parabolic Sheaves |
| title_full_unstemmed | Toward AGT for Parabolic Sheaves |
| title_short | Toward AGT for Parabolic Sheaves |
| title_sort | toward agt for parabolic sheaves |
| url | https://hdl.handle.net/1721.1/145815 |
| work_keys_str_mv | AT negutandrei towardagtforparabolicsheaves |