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Projectively equivariant symbol calculus for bidifferential operators

Fabien Boniver
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Abstract

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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Fabien Boniver. 2000-06-07. Projectively equivariant symbol calculus for bidifferential operators. https://arxiv.org/abs/math/0006047

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