Symplectic Geometries on $T^*\widetilde{G}$, Hamiltonian Group Actions and Integrable Systems

Details Symplectic Geometries on $T^*\widetilde{G}$, Hamiltonian Group Actions and Integrable Systems Symplectic Geometries on $T^*\widetilde{G}$, Hamiltonian Group Actions and Integrable Systems

1992-10-17

arxiv.org/abs/hep-th/9210095v2

J.Geom.Phys. 16 (1995) 168-206

Physics

High Energy Physics

High Energy Physics - Theory

49 pages

Scientific paper

10.1016/0393-0440(94)00027-2

Various Hamiltonian actions of loop groups $\wt G$ and of the algebra $\text{diff}_1$ of first order differential operators in one variable are defined on the cotangent bundle $T^*\wt G$ of a Loop Group. The moment maps generating the $\text{diff}_1$ actions are shown to factorize through those generating the loop group actions, thereby defining commuting diagrams of Poisson maps to the duals of the corresponding centrally extended algebras. The maps are then used to derive a number of infinite commuting families of Hamiltonian flows that are nonabelian generalizations of the dispersive water wave hierarchies. As a further application, sets of pairs of generators of the nonabelian mKdV hierarchies are shown to give a commuting hierarchy on $T^*\wt G$ that contain the WZW system as its first element.

Affiliated with

Also associated with

No associations

Rating

Symplectic Geometries on $T^*\widetilde{G}$, Hamiltonian Group Actions and Integrable Systems does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Symplectic Geometries on $T^*\widetilde{G}$, Hamiltonian Group Actions and Integrable Systems, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Symplectic Geometries on $T^*\widetilde{G}$, Hamiltonian Group Actions and Integrable Systems will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-420271