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

B. Lulek
^{ a}, T. Lulek^{ b}, M. Łabuz^{ c} and J. Milewski^{ d}^{a}East European State Higher School, T. Terleckiego 6, 37-700 Przemyśl, Poland
^{b}Faculty of Physics, Adam Mickiewicz University, Umultowska 85, 61-614 Poznań, Poland
^{c}Department of Theoretical Physics, Faculty of Mathematics and Natural Sciences, University of Rzeszow, S. Pigonia 1, 35-310 Rzeszów, Poland
^{d}Institute of Mathematics, Poznan University of Technology, Piotrowo 3A, 60-965 Poznań, Poland |

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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} × D_{4}. We present also the appropriate irreducible representations of the group. |

DOI: 10.12693/APhysPolA.127.336 PACS numbers: 75.10.Jm, 03.65.Fd, 03.67.Lx, 02.10.Ud, 02.10.De |