Abstract
In this paper, we consider a symplectic leaf that goes through a singular point of the Adler-Gel’fand-Dikii Poisson bracket associated to SL(n,R). We find a finite-dimensional transverse section2 at the singular point and we prove that one can induce a Poisson structure on2 (the transverse structure) that is linearizable and equivalent to the Lie-Poisson structure on sl(n,R)*. This problem is closely related to finding normal forms for nth order scalar differential operators with periodic coefficient. We partially generalize a well-known result for Hill’s operators to the higher order case.
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