  We introduce a method for proving Sum-of-Squares (SoS)/ Lasserre hierarchy
lower bounds when the initial problem formulation exhibits a high degree of
symmetry. Our main technical theorem allows us to reduce the study of the
positive semidefiniteness to the analysis of "well-behaved" univariate
polynomial inequalities.
  We illustrate the technique on two problems, one unconstrained and the other
with constraints. More precisely, we give a short elementary proof of
Grigoriev/Laurent lower bound for finding the integer cut polytope of the
complete graph. We also show that the SoS hierarchy requires a non-constant
number of rounds to improve the initial integrality gap of 2 for the
Min-Knapsack linear program strengthened with cover inequalities.
