Sums of squares in pseudoconvex hypersurfaces and torsion phenomena for Catlin's boundary systems

Given a pseudoconvex hypersurface in C^n and an arbitrary weight, we show the existence of local coordinates in which the polynomial model contains a particularly simple sum of squares of monomials. Our second main result provides a normalization of a part of any Catlin boundary system. We illustrate by an example that this normalization cannot be extended to the rest of the boundary system due to the existence of what we refer to as torsion.