  Extended formulations are an important tool to obtain small (even compact)
formulations of polytopes by representing them as projections of higher
dimensional ones. It is an important question whether a polytope admits a small
extended formulation, i.e., one involving only a polynomial number of
inequalities in its dimension. For the case of symmetric extended formulations
(i.e., preserving the symmetries of the polytope) Yannakakis established a
powerful technique to derive lower bounds and rule out small formulations. We
rephrase the technique of Yannakakis in a group-theoretic framework. This
provides a different perspective on symmetric extensions and considerably
simplifies several lower bound constructions.
