arXiv math/00060472000-06-07math.DGmath.RT

Projectively equivariant symbol calculus for bidifferential operators

Fabien Boniver

备注：: 18 pages

英文摘要：

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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