Amalgams of extremal matroids with no U2,ℓ+2U2,ℓ+2-minor

For an integer ℓ≥2ℓ≥2, let U(ℓ)U(ℓ) be the class of matroids with no U2,ℓ+2U2,ℓ+2-minor. A matroid in U(ℓ)U(ℓ) is extremal if it is simple and has no simple rank-preserving single-element extension in U(ℓ)U(ℓ). An amalgam of two matroids is a simultaneous extension of both on the union of the two ground sets. We study amalgams of extremal matroids in U(ℓ)U(ℓ): we determine which amalgams are in U(ℓ)U(ℓ) and which are extremal in U(ℓ)U(ℓ).