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Résolubilité des opérateurs bi-invariants sur un groupe de Lie semi-simple (Solvability of bi-invariant operators on a semi-simple Lie group). (French) Zbl 0564.22013
Let G be a connected semi-simple Lie group with finite centre, and z a bi-invariant differential operator on G. We give an explicit sufficient condition for z to have a central fundamental solution on G, and for $$zC^{\infty}(G)=C^{\infty}(G).$$ The Casimir operator, which does not always satisfy this condition, is considered separately.

##### MSC:
 2.2e+47 Semisimple Lie groups and their representations
##### Keywords:
bi-invariant differential operator; Casimir operator