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The Full Symmetric Toda Flow and Intersections of Bruhat Cellsстатья
- Авторы: Chernyakov Yuri B., Sharygin Georgy I., Sorin Alexander S., Talalaev Dmitry V.
- Журнал: Symmetry, Integrability and Geometry - Methods and Applications
- Год издания: 2020
- Издательство: Department of Applied Research, Institute of Mathematics of National Academy of Science of Ukraine
- Местоположение издательства: Ukraine
- DOI: 10.3842/sigma.2020.115
- Аннотация: 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 w, w′ in the Weyl group W(g), the corresponding real Bruhat cell Xw intersects with the dual Bruhat cell Yw′ iff w≺w′ in the Bruhat order on W(g). Here g is a normal real form of a semisimple complex Lie algebra gC. Our reasoning is based on the properties of the Toda flows rather than on the analysis of the Weyl group action and geometric considerations.
- Добавил в систему: Талалаев Дмитрий Валерьевич