Communications in Mathematical Physics

, Volume 212, Issue 2, pp 297–321

Factorization Dynamics and Coxeter--Toda Lattices

  • Tim Hoffmann
  • Johannes Kellendonk
  • Nadja Kutz
  • Nicolai Reshetikhin

DOI: 10.1007/s002200000212

Cite this article as:
Hoffmann, T., Kellendonk, J., Kutz, N. et al. Comm Math Phys (2000) 212: 297. doi:10.1007/s002200000212

Abstract:

It is shown that the factorization relation on simple Lie groups with standard Poisson Lie structure restricted to Coxeter symplectic leaves gives an integrable dynamical system. This system can be regarded as a discretization of the Toda flow. In case of SLn the integrals of the factorization dynamics are integrals of the relativistic Toda system. A substantial part of the paper is devoted to the description of symplectic leaves in simple complex Lie groups, its Borel subgroups and their doubles.

Copyright information

© Springer-Verlag Berlin Heidelberg 2000

Authors and Affiliations

  • Tim Hoffmann
    • 1
  • Johannes Kellendonk
    • 1
  • Nadja Kutz
    • 1
  • Nicolai Reshetikhin
    • 1
  1. 1.Fachbereich Mathematik, Sekr. MA 8-5, Technische Universität Berlin, Strasse des 17. Juni 136,¶10623 Berlin, Germany.¶E-mail: timh@sfb288.math.tu-berlin.de; kellen@math.tu-berlin.de; nadja@math.tu-berlin.deDE
  2. 2.Department of Mathematics, University of California at Berkeley, Berkeley, CA 94720, USA.¶E-mail: reshetik@math.berkeley.eduUS