Splitting fields of complex hyperbolic groups: matrix extraction, Hermitian descent, and spectral fields

Angel Cano, Hector Castro, Nikolay Gusevskii

Let $\Gamma <\mathrm{SU}(n,1)$, $n\ge 2$, be Zariski-dense and contain a regular loxodromic element $A$. The splitting-field problem asks how far traces and spectra determine a field of d…