On the basis of comparing eigenvalues of an operator C^(R), that proved useful in distinguishing how off-shell 4D, N = 1 supermultiplets become off-shell 4D, N = 2 supermultiplets, the double tensor supermultiplet is shown to be radically different for other known multiplets. This suggests difficulties, if not impossibilities, to embed it into an off-shell structure.
@article{arxiv.2012.14549,
title = {A Letter Highlighting Matrix Mapping in Minimal 4D, ${\mathbf {\cal N}}$ = 1 On-Shell Supermultiplet Representations},
author = {Delilah E. A. Gates and S. James Gates},
journal= {arXiv preprint arXiv:2012.14549},
year = {2021}
}