Invariant analysis and contractions of symmetric spaces. I. (English) Zbl 0697.53049

Rouvière, François

Compos. Math. 73, No. 3, 241-270 (1990).

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

Keywords:

Campbell-Hausdorff expansion; invariant distribution; symmetric space; G- invariant linear differential operators

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