Why are the Ruijsenaars-Schneider and the Calogero-Moser hierarchies governed by the same tau matrix?

Suris, Yuri B.

doi:10.1016/S0375-9601(96)00897-3

Why are the Ruijsenaars-Schneider and the Calogero-Moser hierarchies governed by the same tau matrix?

Yuri B. Suris
(
- Bremen U.
)

Feb, 1996

18 pages

Published in:

Phys.Lett.A 225 (1997) 253-262

e-Print:

solv-int/9603011 [nlin.SI]

DOI:

10.1016/S0375-9601(96)00897-3

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Abstract:

We demonstrate that in a certain gauge the Lax matrices of the rational and hyperbolic Ruijsenaars--Schneider models have a quadratic

r

-matrix Poisson bracket which is an exact quadratization of the linear

r

--matrix Poisson bracket of the Calogero--Moser models. This phenomenon is explained by a geometric derivation of Lax equations for arbitrary flows of both hierarchies, which turn out to be governed by the same dynamical

R

--operator.

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