Invariant Differential Operators for Non-compact Lie Groups: The Sp(n, IR) Case

Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 36)


In the present paper we continue the project of systematic construction of invariant differential operators on the example of the non-compact algebras sp(n, I​R), in detail for n = 6. Our choice of these algebras is motivated by the fact that they belong to a narrow class of algebras, which we call “conformal Lie algebras”, which have very similar properties to the conformal algebras of Minkowski space-time. We give the main multiplets and the main reduced multiplets of indecomposable elementary representations for n = 6, including the necessary data for all relevant invariant differential operators. In fact, this gives by reduction also the cases for n < 6, since the main multiplet for fixed n coincides with one reduced case for n + 1.


Parabolic Subgroup Verma Module Conformal Weight Hermitian Symmetric Space Discrete Series Representation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.



This work was supported in part by the Bulgarian National Science Fund, grant DO 02-257. The author thanks the Theory Division of CERN for hospitality during the course of this work.


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Copyright information

© Springer Japan 2013

Authors and Affiliations

  1. 1.Theory Division, Department of PhysicsCERNGeneva 23Switzerland
  2. 2.Institute for Nuclear Research and Nuclear EnergySofiaBulgaria

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