  The existence and uniqueness of quantizations that are equivariant with
respect to conformal and projective Lie algebras of vector fields were recently
obtained by Duval, Lecomte and Ovsienko. In order to do so, they computed
spectra of some Casimir operators. We give an explicit formula for those
spectra in the general framework of IFFT-algebras classified by Kobayashi and
Nagano. We also define tree-like subsets of eigenspaces of those operators in
which eigenvalues can be compared to show the existence of IFFT-equivariant
quantizations. We apply our results to prove existence and uniqueness of
quantizations that are equivariant with respect to the infinitesimal action of
the symplectic (resp. pseudo-orhogonal) group on the corresponding Grassmann
manifold of maximal isotropic subspaces.
