With a simplicial G-complex K and a topological pair (X, A), a polyhedral product (X, A)K is associated as a G-invariant subspace of a product space. In this talk, we discuss the existence of a G-equivariant homotopy decomposition of its suspension ∑(X, A)K which further sets up the ground to study the notion of representation stability introduced by Farb and Church in toric topology.

This is a joint work with Jelena Grbić.