Abstract:
Hamiltonian reduction is used to project a trivially integrable system on the Heisenberg double of SU(n,n), to obtain a system of Ruijsenaars type on a suitable quotient space. This system possesses BCn symmetry and is shown to be equivalent to the standard three-parameter BCn hyperbolic Sutherland model in the cotangent bundle limit.
In the 1970s a method was proposed by Olshanetsky and Perelomov, which they called the Projection Method, for generating integrable systems, and in particular for generating systems of "Calogero type". This was then formulated as an example of Hamiltonian reduction by Kazhdan, Kostant and Sternberg. In general, all applications of "Hamiltonian reduction" to systems of Calogero type (which nowadays includes also those of "Ruijsenaars type") are some suitable variation on those original results. I will try to explain a little bit about the background as well as presenting my own result.
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