Analytic discs in symplectic spaces

We develop some symplectic techniques to control the behavior under symplectic transformation of analytic discs A of X = n tangent to a real generic submanifold R and contained in a wedge with edge R. We show that if A is a lift of A to T X and if is a symplectic transformation between neighborhoods of po and qo, then A is orthogonal to po if and only if e A := A is orthogonal to qo. Also we give the (real) canonical form of the couples of hypersurfaces of 2n ' n whose conormal bundles have clean intersection. This generalizes [10] to general dimension of intersection. Combining this result with the quantized action on sheaves of the \tuboidal" symplectic transformation, we show the following: If R, S are submanifolds of X with R S and po 2 T SXjR but ipo =2 T RX, then the conditions codTCS(T CR) = codTS(TR) (resp. codTCS(T CR) = 0) can be characterized as opposite inclusions for the couple of closed half-spaces with conormal bun- dles (T RX) and (T SX) at (po). In x3 we give some partial applications of the above result to the analytic hypoellipticity of CR hyperfunctions on higher codimensional manifolds by the aid of discs (cf. [2], [3] as for the case of hypersurfaces). x1