2001/09/05 by F. Boniver, Boniver, F., P. Mathonet +1
Mathematics · #17B66 #22E46 #81R05 #FOS: Mathematics #Quantum Algebra (math.QA) #Representation Theory (math.RT) #math.QA #math.RT #msc:17B66 #msc:22E46 #msc:81R05
paper · pdf · doi:10.48550/arxiv.math/0109032
18 pages, 1 figure
arxiv created 2001/09/05 · arxiv updated 2009/11/30
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.