University of Cambridge > Talks.cam > Isaac Newton Institute Seminar Series > Poisson-Lie interpretation of a case of the Ruijsenaars duality

Poisson-Lie interpretation of a case of the Ruijsenaars duality

Add to your list(s) Download to your calendar using vCal

If you have a question about this talk, please contact Mustapha Amrani.

Discrete Integrable Systems

By performing a suitable symplectic reduction of the standard Heisenberg double of the group U(n), we give a geometric interpretation of the duality between two real forms of the complex trigonometric Ruijsenaars-Schneider model. The reduced phase space is realized in terms of two global cross sections in the inverse image of the moment map value associated with the reduction. Two natural commutative families of U(n) Poisson-Lie 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.

The talk is based on a forthcoming joint paper with C. Klimcik, which continues arXiv:0809.1509 and arXiv:0901.1983, and will also include a brief discussion of the quantum mechanical version of the construction outlined above.

This talk is part of the Isaac Newton Institute Seminar Series series.

Tell a friend about this talk:

This talk is included in these lists:

Note that ex-directory lists are not shown.

 

© 2006-2020 Talks.cam, University of Cambridge. Contact Us | Help and Documentation | Privacy and Publicity