Yangians, Mirabolic Subalgebras, and Whittaker Vectors
We construct an element in a completion of the universal enveloping algebra of N, which we call the Kirillov projector, that connects the topics of the title: on the one hand, it is defined using the evaluation homomorphism from the Yangian of N, on the other hand, it gives a canonical projection on...
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| Опубліковано в: : | Symmetry, Integrability and Geometry: Methods and Applications |
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| Дата: | 2025 |
| Автор: | |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Інститут математики НАН України
2025
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| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/213188 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Yangians, Mirabolic Subalgebras, and Whittaker Vectors. Artem Kalmykov. SIGMA 21 (2025), 025, 54 pages |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862705092669472768 |
|---|---|
| author | Kalmykov, Artem |
| author_facet | Kalmykov, Artem |
| citation_txt | Yangians, Mirabolic Subalgebras, and Whittaker Vectors. Artem Kalmykov. SIGMA 21 (2025), 025, 54 pages |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | We construct an element in a completion of the universal enveloping algebra of N, which we call the Kirillov projector, that connects the topics of the title: on the one hand, it is defined using the evaluation homomorphism from the Yangian of N, on the other hand, it gives a canonical projection onto the space of Whittaker vectors for any Whittaker module over the mirabolic subalgebra. Using the Kirillov projector, we deduce some categorical properties of Whittaker modules; for instance, we prove a mirabolic analog of Kostant's theorem. We also show that it quantizes a rational version of the Cremmer-Gervais -matrix. As an application, we construct a universal vertex-IRF transformation from the standard dynamical -matrix to this constant one in categorical terms.
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| first_indexed | 2026-03-18T20:22:51Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-213188 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2026-03-18T20:22:51Z |
| publishDate | 2025 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Kalmykov, Artem 2026-02-16T16:35:49Z 2025 Yangians, Mirabolic Subalgebras, and Whittaker Vectors. Artem Kalmykov. SIGMA 21 (2025), 025, 54 pages 1815-0659 2020 Mathematics Subject Classification: 17B37; 17B38 arXiv:2310.06669 https://nasplib.isofts.kiev.ua/handle/123456789/213188 https://doi.org/10.3842/SIGMA.2025.025 We construct an element in a completion of the universal enveloping algebra of N, which we call the Kirillov projector, that connects the topics of the title: on the one hand, it is defined using the evaluation homomorphism from the Yangian of N, on the other hand, it gives a canonical projection onto the space of Whittaker vectors for any Whittaker module over the mirabolic subalgebra. Using the Kirillov projector, we deduce some categorical properties of Whittaker modules; for instance, we prove a mirabolic analog of Kostant's theorem. We also show that it quantizes a rational version of the Cremmer-Gervais -matrix. As an application, we construct a universal vertex-IRF transformation from the standard dynamical -matrix to this constant one in categorical terms. The author would like to thank Roman Bezrukavnikov, Pavel Etingof, Boris Feigin, Michael Finkelberg, Joel Kamnitzer, Vasily Krylov, and Leonid Rybnikov for helpful discussions and explanations, as well as the anonymous referees for their comments. The author would also like to thank the contributors of [41]; this project would not be possible without their libraries. This work was initially supported by the Ministry of Science and Higher Education of the Russian Federation (agreement no. 075–15–2022–287); the majority of it was carried out at the Massachusetts Institute of Technology. The author is very grateful to the Department of Mathematics of MIT for its hospitality and for the opportunity to avoid (a form of) politically motivated persecution in Russia. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Yangians, Mirabolic Subalgebras, and Whittaker Vectors Article published earlier |
| spellingShingle | Yangians, Mirabolic Subalgebras, and Whittaker Vectors Kalmykov, Artem |
| title | Yangians, Mirabolic Subalgebras, and Whittaker Vectors |
| title_full | Yangians, Mirabolic Subalgebras, and Whittaker Vectors |
| title_fullStr | Yangians, Mirabolic Subalgebras, and Whittaker Vectors |
| title_full_unstemmed | Yangians, Mirabolic Subalgebras, and Whittaker Vectors |
| title_short | Yangians, Mirabolic Subalgebras, and Whittaker Vectors |
| title_sort | yangians, mirabolic subalgebras, and whittaker vectors |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/213188 |
| work_keys_str_mv | AT kalmykovartem yangiansmirabolicsubalgebrasandwhittakervectors |