Comptes Rendus
no. 4
Mathematical physics
Integrability of the periodic Kostant–Toda flow on matrix loops of level k
[Intégrabilité du flot périodique de Kostant–Toda sur des boucles de matrices de niveau k]

Présenté par : the Editorial Board

Luen-Chau Li1 ; Zhaohu Nie2
1 Department of Mathematics, Pennsylvania State University, University Park, PA 16802, USA
2 Department of Mathematics and Statistics, Utah State University, Logan, UT 84322-3900, USA
Comptes Rendus. Mathématique, Volume 353 (2015) no. 4, pp. 363-367.

Dans cette note, nous annonçons des résultats sur l'intégrabilité du flot périodique de Kostant–Toda sur des boucles de matrices de niveau k dans sl(n,C).

In this note, we announce results on the Liouville integrability of the periodic Kostant–Toda flow on loops of matrices in sl(n,C) of level k.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2015.01.006
Luen-Chau Li 1 ; Zhaohu Nie 2

1 Department of Mathematics, Pennsylvania State University, University Park, PA 16802, USA
2 Department of Mathematics and Statistics, Utah State University, Logan, UT 84322-3900, USA 
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Luen-Chau Li; Zhaohu Nie. Integrability of the periodic Kostant–Toda flow on matrix loops of level k. Comptes Rendus. Mathématique, Volume 353 (2015) no. 4, pp. 363-367. doi : 10.1016/j.crma.2015.01.006. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2015.01.006/

[1] A. Adler On a trace functional for formal pseudo-differential operators and the symplectic structure of the Korteweg–deVries-type equations, Invent. Math., Volume 50 (1979), pp. 219-248

[2] A. Adler; P. van Moerbeke; P. Vanhaecke Algebraic Integrability, Painleve Geometry and Lie Algebras, Ergebnisse der Mathematik, Springer-Verlag, Berlin, 2004

[3] H.F. Baker Examples of applications of Newton's polygon to the theory of singular points of algebraic functions, Trans. Cambr. Philos. Soc., Volume 15 (1893), pp. 403-450

[4] K. Ben Abdeljelil The integrability of the periodic full Kostant–Toda lattice on a simple Lie algebra, J. Lie Theory, Volume 21 (2011), pp. 929-960

[5] P. Deift; L.C. Li; T. Nanda; C. Tomei The Toda flow on a generic orbit is integrable, Commun. Pure Appl. Math., Volume 39 (1986), pp. 183-232

[6] P. Deift; L.C. Li; C. Tomei Matrix factorizations and integrable systems, Commun. Pure Appl. Math., Volume 42 (1989), pp. 443-521

[7] N. Ercolani; H. Flaschka; S. Singer The geometry of the full Kostant–Toda lattice, Luminy, 1991 (Progr. Math.), Volume vol. 115, Birkhäuser Boston, Boston, MA (1993), pp. 181-225

[8] H. Flaschka The Toda lattice, II: existence of integrals, Phys. Rev. B, Volume 9 (1974), pp. 1924-1925

[9] M. Gekhtman; M. Shapiro Noncommutative and commutative integrability of generic Toda flows in simple Lie algebras, Commun. Pure Appl. Math., Volume 52 (1999), pp. 53-84

[10] A.G. Khovanskii Newton polyhedra and the genus of complete intersections, Funct. Anal. Appl., Volume 12 (1978), pp. 38-46

[11] B. Kostant The solution to a generalized Toda lattice and representation theory, Adv. Math., Volume 34 (1979), pp. 195-338

[12] M. Semenov-Tian-Shansky What is a classical r-matrix?, Funct. Anal. Appl., Volume 17 (1983), pp. 259-272

[13] P. van Moerbeke; D. Mumford The spectrum of difference operators and algebraic curves, Acta Math., Volume 143 (1979), pp. 93-154

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