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Communications in Mathematical Physics

, Volume 138, Issue 2, pp 245–258 | Cite as

Unitarization of a singular representation ofSO(p, q)

  • B. Binegar
  • R. Zierau
Article

Abstract

A geometric construction of a certain singular unitary representation ofSOe(p,q), withp+q even is given. The representation is realized geometrically as the kernel of aSOe(p,q)-invariant operator on a space of sections over a homogeneous space forSOe(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.

Keywords

Neural Network Statistical Physic Complex System Nonlinear Dynamics Quantum Computing 
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Copyright information

© Springer-Verlag 1991

Authors and Affiliations

  • B. Binegar
    • 1
  • R. Zierau
    • 1
  1. 1.Department of MathematicsOklahoma State UniversityStillwaterUSA

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