Identify the unresolved flavored characters of the \(SU(2)/\mathbb{Z}_4\) quotient

Determine whether the unflavored solutions with indicial roots \(\alpha=0\) and \(\alpha=\frac18\) for the \(SU(2)/\mathbb{Z}_4\) quotient correspond to legitimate ordinary-module characters, and obtain their flavored closed forms if they do.

Background

For the SU(2)/Z4SU(2)/\mathbb{Z}_4 quotient, the paper identifies several flavored characters and constructs an unflavored MLDE. The indicial roots include $0$ and 18\frac18, but the corresponding flavored solutions are not explicitly determined.

This leaves open whether those solutions arise from genuine ordinary modules or are merely formal solutions of the MLDE. Establishing their status is necessary for a complete character classification.

References

We have not identified the flavored solution in closed form for \alpha = 0, \frac{1}{8}, nor can we rule out their correspondence to legitimate characters.

— Rank-one 4d $\mathcal N=3$ SCFTs: Schur index, VOA modules, and modularity  (2609.10685 - Guo et al., 9 Sep 2026) in Section 4, subsection “Closed-form index and non-vacuum characters”