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SUMMARY:Poisson-Lie interpretation of a case of the Ruijsenaars duality - 
 Feher\, L (KFKI)
DTSTART:20090324T153000Z
DTEND:20090324T163000Z
UID:TALK17540@talks.cam.ac.uk
CONTACT:Mustapha Amrani
DESCRIPTION:By performing a suitable symplectic reduction of the standard 
 Heisenberg double of the group U(n)\, we give a geometric interpretation o
 f the duality between two real forms of the complex trigonometric Ruijsena
 ars-Schneider model. The reduced phase space is realized in terms of two g
 lobal cross sections in the inverse image of the moment map value associat
 ed with the reduction. Two natural commutative families of U(n) Poisson-Li
 e symmetric Hamiltonian flows on the double descend upon reduction to the 
 respective commuting flows of the mutually dual models. The reduced flows 
 are automatically complete\, and reproduce the original direct completion 
 of the dual flows due to Ruijsenaars. \n\nThe talk is based on a forthcomi
 ng joint paper with C. Klimcik\, which continues arXiv:0809.1509 and arXiv
 :0901.1983\, and will also include a brief discussion of the quantum mecha
 nical version of the construction outlined above.
LOCATION:Seminar Room 1 Newton Institute
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