Transverse Poisson structures of coadjoint orbits
The author studies nonlinear Poisson brackets associated with orbits through nilpotent conjugacy classes in the Lie algebra \(\text{gl}(n,\mathbb{C})\). The methods involve transverse Poisson structures, Dirac brackets, etc. For \(n < 7\) the degree of the transverse Poisson structure is determined. Some conjectures are formulated and some of them are proved in several special cases.
scientific article; zbMATH DE number 889862