Braid Group Action on Affine Yangian
We study braid group actions on Yangians associated with symmetrizable Kac-Moody Lie algebras. As an application, we focus on the affine Yangian of type A and use the action to prove that the image of the evaluation map contains the diagonal Heisenberg algebra inside ĝlN.
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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Date: | 2019 |
| Main Author: | |
| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2019
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/210055 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | Braid Group Action on Affine Yangian / R. Kodera // Symmetry, Integrability and Geometry: Methods and Applications. — 2019. — Т. 15. — Бібліогр.: 18 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862687452335964160 |
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| author | Kodera, R. |
| author_facet | Kodera, R. |
| citation_txt | Braid Group Action on Affine Yangian / R. Kodera // Symmetry, Integrability and Geometry: Methods and Applications. — 2019. — Т. 15. — Бібліогр.: 18 назв. — англ. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | We study braid group actions on Yangians associated with symmetrizable Kac-Moody Lie algebras. As an application, we focus on the affine Yangian of type A and use the action to prove that the image of the evaluation map contains the diagonal Heisenberg algebra inside ĝlN.
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| first_indexed | 2025-12-07T21:24:13Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-210055 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-07T21:24:13Z |
| publishDate | 2019 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Kodera, R. 2025-12-02T09:29:56Z 2019 Braid Group Action on Affine Yangian / R. Kodera // Symmetry, Integrability and Geometry: Methods and Applications. — 2019. — Т. 15. — Бібліогр.: 18 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 17B10; 17B37; 17B67 arXiv: 1805.01621 https://nasplib.isofts.kiev.ua/handle/123456789/210055 https://doi.org/10.3842/SIGMA.2019.020 We study braid group actions on Yangians associated with symmetrizable Kac-Moody Lie algebras. As an application, we focus on the affine Yangian of type A and use the action to prove that the image of the evaluation map contains the diagonal Heisenberg algebra inside ĝlN. The author would like to thank Yoshihisa Saito for suggesting that he study braid group action on the affine Yangian. Discussions with him improved the contents of this paper. He also thanks Nicolas Guay for telling him the reference [3] and the referees for their helpful comments. This work was supported by JSPS KAKENHI Grant Numbers 26287004, 17H06127, 18K13390, and the Kyoto University Foundation. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Braid Group Action on Affine Yangian Article published earlier |
| spellingShingle | Braid Group Action on Affine Yangian Kodera, R. |
| title | Braid Group Action on Affine Yangian |
| title_full | Braid Group Action on Affine Yangian |
| title_fullStr | Braid Group Action on Affine Yangian |
| title_full_unstemmed | Braid Group Action on Affine Yangian |
| title_short | Braid Group Action on Affine Yangian |
| title_sort | braid group action on affine yangian |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/210055 |
| work_keys_str_mv | AT koderar braidgroupactiononaffineyangian |