SO(2n,C)-character varieties are not varieties of characters

We prove that for n≥2 and all groups Γ of corank ≥2 the coordinate rings of SO(2n,C)-character varieties of Γ are not generated by trace functions nor generalized trace functions τ_ϕ,γ, sending ρ:Γ→SO(2n,C) to trϕρ(γ), for an arbitrary representation ϕ of SO(2n,C) and any γ∈Γ. Furthermore, we give examples of non-conjugate completely reducible representations undistinguishable by generalized trace functions. Hence, SO(2n,C)-character varieties are not varieties of characters! However, we also prove that any generic SO(2n,C)-representation of a free group can be distinguished from all non-equivalent representations by trace functions and by a single generalized trace function.