Analysis on the minimal representation of O(p,q) I. Realization via conformal geometry |
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Authors: | Toshiyuki Kobayashi,Bent
rsted |
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Affiliation: | a RIMS, Kyoto University, Sakyo-ku, Kyoto 606-8502, Japan;b Department of Mathematics and Computer Science, SDU - Odense University, Campusvej 55, Odense M, DK-5230, Denmark |
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Abstract: | This is the first in a series of papers devoted to an analogue of the metaplectic representation, namely the minimal unitary representation of an indefinite orthogonal group; this representation corresponds to the minimal nilpotent coadjoint orbit in the philosophy of Kirillov–Kostant. We begin by applying methods from conformal geometry of pseudo-Riemannian manifolds to a general construction of an infinite-dimensional representation of the conformal group on the solution space of the Yamabe equation. By functoriality of the constructions, we obtain different models of the unitary representation, as well as giving new proofs of unitarity and irreducibility. The results in this paper play a basic role in the subsequent papers, where we give explicit branching formulae, and prove unitarization in the various models. |
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Keywords: | Minimal unitary representation Conformal geometry |
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