The Full Symmetric Toda Flow and Intersections of Bruhat Cells
| dc.contributor.author | Chernyakov, Yuri B. | |
| dc.contributor.author | Sharygin, Georgy I. | |
| dc.contributor.author | Sorin, Alexander S. | |
| dc.contributor.author | Talalaev, Dmitry V. | |
| dc.date.accessioned | 2025-12-22T09:24:28Z | |
| dc.date.issued | 2020 | |
| dc.description.abstract | 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. | |
| dc.description.sponsorship | The authors thank Sergey Loktev, Vladimir Rubtsov, and Evgeniy Smirnov for useful discussions. The authors would like to express their gratitude to the anonymous referee, whose remarks have helped us to improve the presentation of this paper. The work of Yu.B. Chernyakov was partly supported by the grant RFBR-18-02-01081. The work of G.I. Sharygin was partly supported by the grant RFBR-18-01-00398. The work of D.V. Talalaev was partly supported by the grant Leader(math) 20-7-1-21-1 of the foundation for the advancement of theoretical physics and mathematics BASIS and within the framework of a development program for the Regional Scienti c and Educational Mathematical Center of the Yaroslavl State University with nancial support from the Ministry of Science and Higher Education of the Russian Federation (Agreement No. 075-02-2020-1514/1 additional to the agreement on provision of subsidies from the federal budget No. 075-02-2020-1514). | |
| dc.identifier.citation | 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 | |
| dc.identifier.doi | https://doi.org/10.3842/SIGMA.2020.115 | |
| dc.identifier.issn | 1815-0659 | |
| dc.identifier.other | 2020 Mathematics Subject Classification: 22E15; 70H06 | |
| dc.identifier.other | arXiv:1810.09622 | |
| dc.identifier.uri | https://nasplib.isofts.kiev.ua/handle/123456789/211005 | |
| dc.language.iso | en | |
| dc.publisher | Інститут математики НАН України | |
| dc.relation.ispartof | Symmetry, Integrability and Geometry: Methods and Applications | |
| dc.status | published earlier | |
| dc.title | The Full Symmetric Toda Flow and Intersections of Bruhat Cells | |
| dc.type | Article |
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