Summer School and Conference on Modern Mathematical Physics

9 - 19 September 2012, Belgrade, Serbia

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Vladimir Dobrev

Invariant differential operators for noncompact Lie groups

In the present talk I review the progress of the project of systematic construction of invariant differential operators for non-compact Lie groups on the example of the class of conformal Lie groups. The latter are called also Hermitian symmetric spaces of tube type, and also Euclidean Jordan groups. We extend our approach by considering non-compact Lie algebras parabolically related conformal Lie algebras. We show more details for the non-compact Lie groups SO(n,2) and SO(p,q), SU(n,n), Sp(n,R), E_{7(-25)} and E_{6(-14)}, where we give the main multiplets of indecomposable elementary representations, including the necessary data for all relevant invariant differential operators.