IFFT-Equivariant Quantizations

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dc.creatorBoniver, F.
dc.creatorMathonet, P.
dc.date2001-09-05
dc.date.accessioned2026-07-07T04:43:16Z
dc.date.available2026-07-07T04:43:16Z
dc.descriptionThe 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.
dc.description18 pages, 1 figure
dc.identifierhttps://arxiv.org/abs/math/0109032
dc.identifierhttp://arxiv.org/abs/math/0109032
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/62147
dc.subjectRepresentation Theory
dc.subjectQuantum Algebra
dc.subject17B66;22E46;81R05
dc.titleIFFT-Equivariant Quantizations
dc.typetext

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