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Generalization of Harish-Chandra’s basic theorem for Riemannian symmetric spaces of non-compact type. (English) Zbl 1154.22019

Summary: A basic exact sequence by Harish-Chandra related to the invariant differential operators on a Riemannian symmetric space \(G/K\) is generalized for each \(K\)-type in a certain class which we call ‘single-petaled’. The argument also includes a further generalization of Broer’s generalization of the Chevalley restriction theorem.

MSC:

22E46 Semisimple Lie groups and their representations
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