Representability conjecture for graded automorphism functors of N-Lie conformal superalgebra forms

Let $N\in\{1,2,3,4\}$, let $\mathcal{A}$ be a complex $N$-Lie conformal superalgebra, and let $\mathcal{L}$ be an $\widehat{\mathcal{S}}/\mathcal{R}$-form of $\mathcal{A}\otimes_{\mathbb{C}}\mathcal{R}$. Let $\mathbf{GrAut}(\mathcal{L})$ be the naturally defined subgroup functor of the $\mathcal{R}$-group functor $\mathbf{Aut}(\mathcal{L})$ preserving the grading, where $\mathcal{L}=\bigoplus_{n\in\mathbb{N}}\widehat{\partial}^{n}\mathcal{V}$ for a suitable degree-zero subspace $\mathcal{V}$. Representability conjecture. If $N\neq4$, the $\mathcal{R}$-group functor $\mathbf{GrAut}(\mathcal{L})$ is representable by an affine group scheme of finite type whose connected component of the identity is simple in the sense of SGA 3. This conjecture concerns the algebraic-group structure of graded automorphisms of forms of these conformal superalgebras; the case $N=4$ is excluded and treated separately in the source.