Resumen de A converse to the Grace�Walsh�Szego theorem

Petter Brändén, David G. Wagner

• We prove that the symmetrizer of a permutation group preserves stability if and only if the group is orbit homogeneous. A consequence is that the hypothesis of permutation invariance in the Grace�Walsh�Szego Coincidence Theorem cannot be relaxed. In the process we obtain a new characterization of the Grace-like polynomials, introduced by D. Ruelle, and prove that the class of such polynomials can be endowed with a natural multiplication.