  We prove the uniqueness of the martingale problem associated to some
degenerate operators. The key point is to exploit the strong parallel between
the new technique introduced by Bass and Perkins (From Probability to Geometry,
vol. in honor of J.M Bismut (2009)) to prove uniqueness of the martingale
problem in the framework of non degenerated elliptic operators and the Mc Kean
and Singer (Journal of Diff. Geometry, 1967) parametrix approach to the density
expansion that has previously been extended to the degenerate setting that we
consider (see Delarue and Menozzi, Journal of Funct. Analysis, 2010).
