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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.