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Invariant analysis and contractions of symmetric spaces. I. (English) Zbl 0697.53049
The main problem of this paper is the following: is it possible to transform an invariant differential operator on a homogeneous space into a constant coefficient differential operator on some vector space? The author considers the case of a simply connected symmetric space $$M=G/H$$ with the algebra $${\mathbb{D}}(M)$$ of all G-invariant linear differential operators on M. For such spaces a function e(x,y) of two tangent vectors at the origin of M, obtained from the corresponding infinitesimal structure of Lie triple system is defined and studied. The study is based on the idea of contractions of M into its tangent space.
Reviewer: A.Fleischer

MSC:
 53C35 Differential geometry of symmetric spaces 43A85 Harmonic analysis on homogeneous spaces 58J70 Invariance and symmetry properties for PDEs on manifolds 17B60 Lie (super)algebras associated with other structures (associative, Jordan, etc.) 17A40 Ternary compositions
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