Formalite G∞ adaptee et star-representations sur des sous-varietes coisotropes

الأصل · EN

Let X be a Poisson manifold and C a coisotropic submanifold and let I be the vanishing ideal of C. In this work we want to construct a star product * on X such that I[[lambda]] is a left ideal for *. Thus we obtain a representation of the star product algebra A[[lambda]] = C∞(X)[[lambda]] on B[[lambda]] = A[[lambda]] / I[[lambda]] deforming the usual representation of A on the functions on C. The result follows from a generalization of Tamarkin's formality adapted to the submanifold C. We show that in the case X = Rⁿ and C = Rⁿ⁻ˡ with l > 1 there are no obstructions to this formality.