An integral transform in L2-cohomology for the ladder representations of U(p, q) |
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Authors: | Lisa A Mantini |
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Institution: | Department of Mathematics, Wellesley College, Wellesley, Massachusetts 02181 USA |
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Abstract: | Starting from the realization of the Fock space as L2-cohomology of p + q, 0,p(p + q) = ⊕m?m0,p(p + q), an integral transform is constructed which is a direct-image mapping from m0,p(p + q) into the space of holomorphic sections of some vector bundle Em over M ≈ U(p, q)/(U(q) × U(p)), m ? 0. The transform intertwines the natural actions of U(p, q) and is injective if m ? 0, so it provides a geometric realization of the ladder representations of U(p, q). The sections in the image of the transform satisfy certain linear differential equations, which are explicitly described. For example, Maxwell's equations are of this form if p = q = 2 and m = 2. Thus, this transform is analogous to the Penrose correspondence. |
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