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The exact Bethe eigenfunctions for the heptagonal ring within the isotropicXXX model exhibit a doubly degenerated energy level in the three-deviationsector at the centre of the Brillouin zone. We demonstrate an explicitconstruction of these eigenfunctions by use of algebraic Bethe Ansatz, andpoint out a relation of degeneracy to parity conservation, applied to theconfiguration of strings for these eigenfunctions. Namely, the internalstructure of the eigenfunctions (the 2-string and the 1-string, with oppositequasimomenta) admits generation of two mutually orthogonal eigenfunctions dueto the fact that the strings which differ by their length are distinguishableobjects.

Internal parity symmetry and degeneracy of Bethe Ansatz strings in the isotropic heptagonal magnetic ring