Abstract
We consider the spaces F-mu of polynomial mu-densities on the line as sl(2)-modules and then we compute the cohomological spaces H-diff(1) sl(2), D-lambda,D-mu), where mu is an element of R, (lambda) over bar = (lambda(1), ...,lambda(n)) is an element of R-n and D-lambda,D-mu is the space of n-ary differential operators from F-lambda 1 circle times ...circle times F-lambda n to F-mu.