Lie superalgebra correspondence for E-type quivers

Determine which Lie superalgebras, if any, correspond to the E-type quivers with potentials associated with the tetrahedral group A_4, the octahedral group S_4, and the icosahedral group A_5 in SO(3,\mathbb{C}).

Background

The paper identifies several families of quivers with potentials arising from generalized conifolds and finite subgroups of SO(3,\mathbb{C}) with untwisted affine Lie superalgebras of types A, B, and D. It also discusses the exceptional E-type quivers associated with the tetrahedral, octahedral, and icosahedral groups. While the corresponding affine Lie superalgebras for the A-, B-, and D-type examples are related to established constructions, the paper does not identify any Lie superalgebra associated with the E-type quivers. Establishing such a correspondence would complete the proposed Lie-superalgebraic interpretation of these examples.

References

It is unclear to the author which Lie superalgebras, if any, correspond to the $E$-type quivers with potentials associated with the Tetrahedral group $A_4$, Octahedral group $S_4$ and Icosahedral group $A_5$ in $SO(3,C)$.

— Injectivity of specialization maps in critical cohomology  (2610.11565 - Cao, 8 Oct 2026) in Appendix A, Section \ref{sect on appendix A} (Recognition by Lie superalgebras)