On the cohomology of sl(m+1,R) acting on differential operators and sl(m+1,R)-equivariant symbol
Abstract
Description
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.
LateX file, 20 pages
LateX file, 20 pages