IFFT-Equivariant Quantizations

Details IFFT-Equivariant Quantizations IFFT-Equivariant Quantizations

2001-09-05

arxiv.org/abs/math/0109032v1

Mathematics

Representation Theory

18 pages, 1 figure

Scientific paper

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.

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