Projectively equivariant symbol calculus for bidifferential operators
Abstract
Description
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.
18 pages
18 pages