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CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:Poisson-Lie interpretation of a case of the Ruijse
naars duality - Feher\, L (KFKI)
DTSTART;TZID=Europe/London:20090324T153000
DTEND;TZID=Europe/London:20090324T163000
UID:TALK17540AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/17540
DESCRIPTION:By performing a suitable symplectic reduction of t
he standard Heisenberg double of the group U(n)\,
we give a geometric interpretation of the duality
between two real forms of the complex trigonometri
c Ruijsenaars-Schneider model. The reduced phase s
pace is realized in terms of two global cross sect
ions in the inverse image of the moment map value
associated with the reduction. Two natural commuta
tive families of U(n) Poisson-Lie symmetric Hamilt
onian flows on the double descend upon reduction t
o the respective commuting flows of the mutually d
ual models. The reduced flows are automatically co
mplete\, and reproduce the original direct complet
ion of the dual flows due to Ruijsenaars. \n\nThe
talk is based on a forthcoming joint paper with C.
Klimcik\, which continues arXiv:0809.1509 and arX
iv:0901.1983\, and will also include a brief discu
ssion of the quantum mechanical version of the con
struction outlined above.
LOCATION:Seminar Room 1 Newton Institute
CONTACT:Mustapha Amrani
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