Some news in the question of invariants and Stolovich-Verstringe normal form

We present some new statements in the theory of invariants of representarions of the group SL(2). An application to an analyticity proof of the Stolovich-Verstringe nornal for for  a vector field singularity with nilpotent linear part will be given.

This is a new version of and old work with E. Stróżyna.