Equivariant semidefinite lifts of regular polygons

Understand

Given a polytope P in $\mathbb{R}^n$, we say that P has a positive semidefinite lift (psd lift) of size d if one can express P as the linear projection of an affine slice of the positive semidefinite cone $\mathbf{S}^d_+$.

• If a polytope P has symmetry, we can consider equivariant psd lifts, i.e.
• those psd lifts that respect the symmetry of P.
• One of the simplest families of polytopes with interesting symmetries are regular polygons in the plane, which have played an important role in the study of linear programming lifts (or extended formulations).