TY - JOUR
T1 - Factorization dynamics and Coxeter-Toda lattices
AU - Hoffmann, Tim
AU - Kellendonk, Johannes
AU - Kutz, Nadja
AU - Reshetikhin, Nicolai
PY - 2000
Y1 - 2000
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=0034349027&partnerID=8YFLogxK
U2 - 10.1007/s002200000212
DO - 10.1007/s002200000212
M3 - Article
AN - SCOPUS:0034349027
SN - 0010-3616
VL - 212
SP - 297
EP - 321
JO - Communications in Mathematical Physics
JF - Communications in Mathematical Physics
IS - 2
ER -