On the Liouville integrability of the periodic Kostant-Toda flow on matrix loops of level \(k\) (Q529636)
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scientific article; zbMATH DE number 6721420
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the Liouville integrability of the periodic Kostant-Toda flow on matrix loops of level \(k\) |
scientific article; zbMATH DE number 6721420 |
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On the Liouville integrability of the periodic Kostant-Toda flow on matrix loops of level \(k\) (English)
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19 May 2017
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The authors study the periodic Kostant-Toda flow on certain coadjoint orbits of the loop group associated to \(\mathrm{sl}(n,\mathbb{C})\). These coadjoint orbits can be identified with coadjoint orbits of a suitable semidirect product of finite-dimensional Lie groups. They show that the above Kostant-Toda flow is Liouville integrable, thus proving a conjecture of \textit{K. Ben Abdeljelil} [J. Lie Theory 21, No. 4, 929--960 (2011; Zbl 1264.17018)].
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Kostant-Toda flow
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loop group
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Liouville integrability
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