urf-sg-representation.md

Representation-Theoretic Form of the URF-SG Wall

Let G be the full symmetry group of the base structure.

Let A commute with the unitary representation ρ(G).

Then every admissible perturbation V must lie in: End_G(H) = { T : H → H | T ρ(g) = ρ(g) T ∀ g ∈ G }

The wall is:

Does there exist V ∈ End_G(H) such that Π V Π ≠ 0 ?

Equivalently:

Does the trivial representation occur in End(Ek ⊕ Ek+1) restricted to End_G(H) ?