تقرير
The Full Symmetric Toda Flow and Intersections of Bruhat Cells
| العنوان: | The Full Symmetric Toda Flow and Intersections of Bruhat Cells |
|---|---|
| المؤلفون: | Chernyakov, Yuri B., Sharygin, Georgy I., Sorin, Alexander S., Talalaev, Dmitry V. |
| المصدر: | SIGMA 16 (2020), 115, 8 pages |
| سنة النشر: | 2018 |
| المجموعة: | Mathematics High Energy Physics - Theory Mathematical Physics Nonlinear Sciences |
| مصطلحات موضوعية: | Mathematics - Representation Theory, High Energy Physics - Theory, Mathematical Physics, Nonlinear Sciences - Exactly Solvable and Integrable Systems |
| الوصف: | 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 $W(\mathfrak g)$, the corresponding real Bruhat cell $X_w$ intersects with the dual Bruhat cell $Y_{w'}$ iff $w\prec w'$ in the Bruhat order on $W(\mathfrak g)$. Here $\mathfrak g$ is a normal real form of a semisimple complex Lie algebra $\mathfrak g_\mathbb C$. Our reasoning is based on the properties of the Toda flows rather than on the analysis of the Weyl group action and geometric considerations. Comment: 8 pages |
| نوع الوثيقة: | Working Paper |
| DOI: | 10.3842/SIGMA.2020.115 |
| URL الوصول: | http://arxiv.org/abs/1810.09622 |
| رقم الأكسشن: | edsarx.1810.09622 |
| قاعدة البيانات: | arXiv |
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