The Full Symmetric Toda Flow and Intersections of Bruhat Cells
In this short note, we show that the Bruhat cells in real normal forms of semisimple Lie algebras enjoy the same property as their complex analogs: for any two elements , ′ in the Weyl group (), the corresponding real Bruhat cell intersects with the dual Bruhat cell ′ iff ≺ ′ in the Bruhat order o...
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| Опубліковано в: : | Symmetry, Integrability and Geometry: Methods and Applications |
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| Дата: | 2020 |
| Автори: | , , , |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Інститут математики НАН України
2020
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| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/211005 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | The Full Symmetric Toda Flow and Intersections of Bruhat Cells. Yuri B. Chernyakov, Georgy I. Sharygin, Alexander S. Sorin and Dmitry V. Talalaev. SIGMA 16 (2020), 115, 8 pages |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| Резюме: | In this short note, we show that the Bruhat cells in real normal forms of semisimple Lie algebras enjoy the same property as their complex analogs: for any two elements , ′ in the Weyl group (), the corresponding real Bruhat cell intersects with the dual Bruhat cell ′ iff ≺ ′ in the Bruhat order on (). Here is a normal real form of a semisimple complex Lie algebra ℂ. Our reasoning is based on the properties of the Toda flows rather than on the analysis of the Weyl group action and geometric considerations.
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| ISSN: | 1815-0659 |