Quantum integrability for the Kovalevsky top

Abstract

LetN be a differentiable manifold of dimension n. LetM = T ∗N be the cotangent bundle of N , and denote by σ the natural symplectic form on M . In local coordinates q = (q1, . . . qn) on N and pi = ∂ ∂qi (viewed as function on M) we have σ = ∑ dpi∧dqi. For f ∈ C ∞(M) the hamiltonian vector field vf on M is defined by df(·) = −σ(vf , ·). For this sign convention we have [vf , vg] = v{f,g} (1.1) with the Poisson bracket {f, g} of f, g ∈ C∞(M) defined by {f, g} = vf (g) = σ(vf , vg), or in local coordinates {f, g} = ∑ (