Biquantization techniques for computing characters of differential operators on Lie groups

We compare the character of the algebra (U(g)/U(g)h(lambda))(h), as used by Fujiwara and Corwin and Greenleaf, with the character produced from biquantization techniques applied in the Lie case by Cattaneo and Torossian. We prove that up to a smaller (specialization) algebra, these two characters are the same. An old example is also treated and it is proved that we now get more information about the question of when the symmetrization is an isomorphism of algebras. (C) 2010 Academie des sciences. Published by Elsevier Masson SAS. All rights reserved.