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Invariant differential operators on Grassmann manifolds. (English) Zbl 0613.58038
The algebra D(G/H) of G-invariant differential operators on the manifold G/H (H closed subgroup of the Lie group G) is computed for the case: G \(= the\) group M(n) of rigid motions of \(R^ n\), H \(= the\) subgroup leaving invariant a certain p-plane in \(R^ n\). Hence \(G/H=G(p,n) = space\) of p- planes in \(R^ n\) (p,n arbitrary). It is shown that D(G(p,n)) is an algebra with \(\min (p+1,n-p)\) algebraically independent generators.
Reviewer: S.Andersson

MSC:
58J70 Invariance and symmetry properties for PDEs on manifolds
43A85 Harmonic analysis on homogeneous spaces
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