Irredundance in Eigenvalue Problems

On the twisted octonionic eigenvalue problem and some sextics hypersurfaces related to the Cartan cubic

We revisit the octonionic eigenvalue problem from a geometric perspective. In particular, we study a tautological sheaf defined on a sextic related to this problem, the Ogievetskiî-Dray-Manogue sextic. We then define and study a twisted version of the octonionic eigenvalue problem. A new sextic arises in this setting and we study the corresponding tautological sheaf supported on it. This twisted version of the octonionic eigenvalue problem is eminently more symmetric than the original one, as reflected by the last result we prove in this paper : the automorphism group of the twisted octonionic…