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 |
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| 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| Резюме: | 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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| ISSN: | 1815-0659 |