Point Group Interpretation of Galois Symmetry of Bethe Ansatz Solutions of Magnetic Pentagonal Ring

Exact solutions of the eigenproblem of the magnetic pentagonal ring exhibit the arithmetic symmetry expressed in terms of a Galois group of a finite extension of the prime field Q of rationals. We propose here a geometric interpretation of this symmetry in the interior of the Brillouin zone, in terms of point groups. Explicitly, it is a subgroup of the direct product C-4 x D-4. We present also the appropriate irreducible representations of the group.