On the cohomology of sl(m+1,R) acting on differential operators and sl(m+1,R)-equivariant symbol

Details On the cohomology of sl(m+1,R) acting on differential operators and sl(m+1,R)-equivariant symbol On the cohomology of sl(m+1,R) acting on differential operators and sl(m+1,R)-equivariant symbol

1998-01-27

arxiv.org/abs/math/9801121v1

Mathematics

Differential Geometry

LateX file, 20 pages

Scientific paper

One computes the cohomology of the projective embedding of sl(m+1,R) acting on the differential operators on densities on R^m of various weights. This cohomology is non vanishing only for some special critical values of the weights. This allows us first to explain some strange feature pointed out by Gargoubi in his classification if the module of differential operators on the line. This also allows us to provide a so called sl(m+1,R) invariant symbol for differential operators acting on densities of non critical weights.

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