On a canonical form of a 3×3 Hermitian matrix over the ring of integral split octonions

We show that a 3×3 Hermitian matrix over the ring of integral split octonions has a unique canonical diagonal form under the action of the group . This confirms the conjecture of J. Maldacena, G. Moore, and A. Strominger [hep-th/9903163] on a standard form of a charge vector.