Projectively equivariant symbol calculus for bidifferential operators

Details Projectively equivariant symbol calculus for bidifferential operators Projectively equivariant symbol calculus for bidifferential operators

2000-06-07

arxiv.org/abs/math/0006047v1

Mathematics

Differential Geometry

18 pages

Scientific paper

We prove the existence and uniqueness of a *projectively equivariant symbol map*, which is an isomorphism between the space of bidifferential operators acting on tensor densities over $R^n$ and that of their symbols, when both are considered as modules over an imbedding of $sl(n+1,\R)$ into polynomial vector fields. The coefficients of the bidifferential operators are densities of an arbitrary weight. We obtain the result for all values of this weight, except for a set of critical ones, which does not contain 0. In the case of second order operators, we give explicit formulas and examine in detail the critical values.

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