[Intégrabilité du flot périodique de Kostant–Toda sur des boucles de matrices de niveau k]
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 .
In this note, we announce results on the Liouville integrability of the periodic Kostant–Toda flow on loops of matrices in of level k.
Accepté le :
Publié le :
@article{CRMATH_2015__353_4_363_0,
author = {Li, Luen-Chau and Nie, Zhaohu},
title = {Integrability of the periodic {Kostant{\textendash}Toda} flow on matrix loops of level \protect\emph{k}},
journal = {Comptes Rendus. Math\'ematique},
pages = {363--367},
publisher = {Elsevier},
volume = {353},
number = {4},
year = {2015},
doi = {10.1016/j.crma.2015.01.006},
language = {en},
url = {http://www.numdam.org/articles/10.1016/j.crma.2015.01.006/}
}
TY - JOUR AU - Li, Luen-Chau AU - Nie, Zhaohu TI - Integrability of the periodic Kostant–Toda flow on matrix loops of level k JO - Comptes Rendus. Mathématique PY - 2015 SP - 363 EP - 367 VL - 353 IS - 4 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2015.01.006/ DO - 10.1016/j.crma.2015.01.006 LA - en ID - CRMATH_2015__353_4_363_0 ER -
%0 Journal Article %A Li, Luen-Chau %A Nie, Zhaohu %T Integrability of the periodic Kostant–Toda flow on matrix loops of level k %J Comptes Rendus. Mathématique %D 2015 %P 363-367 %V 353 %N 4 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.crma.2015.01.006/ %R 10.1016/j.crma.2015.01.006 %G en %F CRMATH_2015__353_4_363_0
Li, Luen-Chau; Nie, Zhaohu. Integrability of the periodic Kostant–Toda flow on matrix loops of level k. Comptes Rendus. Mathématique, Tome 353 (2015) no. 4, pp. 363-367. doi : 10.1016/j.crma.2015.01.006. http://www.numdam.org/articles/10.1016/j.crma.2015.01.006/
[1] 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] Algebraic Integrability, Painleve Geometry and Lie Algebras, Ergebnisse der Mathematik, Springer-Verlag, Berlin, 2004
[3] 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] The integrability of the periodic full Kostant–Toda lattice on a simple Lie algebra, J. Lie Theory, Volume 21 (2011), pp. 929-960
[5] The Toda flow on a generic orbit is integrable, Commun. Pure Appl. Math., Volume 39 (1986), pp. 183-232
[6] Matrix factorizations and integrable systems, Commun. Pure Appl. Math., Volume 42 (1989), pp. 443-521
[7] The geometry of the full Kostant–Toda lattice, Luminy, 1991 (Progr. Math.), Volume vol. 115, Birkhäuser Boston, Boston, MA (1993), pp. 181-225
[8] The Toda lattice, II: existence of integrals, Phys. Rev. B, Volume 9 (1974), pp. 1924-1925
[9] Noncommutative and commutative integrability of generic Toda flows in simple Lie algebras, Commun. Pure Appl. Math., Volume 52 (1999), pp. 53-84
[10] Newton polyhedra and the genus of complete intersections, Funct. Anal. Appl., Volume 12 (1978), pp. 38-46
[11] The solution to a generalized Toda lattice and representation theory, Adv. Math., Volume 34 (1979), pp. 195-338
[12] What is a classical r-matrix?, Funct. Anal. Appl., Volume 17 (1983), pp. 259-272
[13] The spectrum of difference operators and algebraic curves, Acta Math., Volume 143 (1979), pp. 93-154
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