Abstract
A geometric construction of a certain singular unitary representation ofSO e(p,q), withp+q even is given. The representation is realized geometrically as the kernel of aSO e(p,q)-invariant operator on a space of sections over a homogeneous space forSO e(p,q). TheK-structure of these representations is elucidated and we demonstrate their unitarity by explicitly writing down anso(p,q) positive definite hermitian form. Finally, we demonstrate that the annihilator inU[g] of this representation is the Joseph ideal, which is the maximal primitive ideal associated with the minimal coadjoint orbit.
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Communicated by H. Araki
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Binegar, B., Zierau, R. Unitarization of a singular representation ofSO(p, q) . Commun.Math. Phys. 138, 245–258 (1991). https://doi.org/10.1007/BF02099491
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DOI: https://doi.org/10.1007/BF02099491