On Symmetries of Finite Geometries
<|reference_start|>On Symmetries of Finite Geometries: The isospectral set of the Dirac matrix D=d+d* consists of orthogonal Q for which Q* D Q is an equivalent Dirac matrix. It can serve as the symmetry of a finite geometry G. The symmetry is a subset of the orthogonal group or unitary group and isospectral Lax deformations produce commuting flows d/dt D=[B(g(D)),D] on this symmetry space. In this note, we remark that like in the Toda case, D_t=Q_t* D_0 Q_t with exp(-t g(D))=Q_t R_t solves the Lax system.<|reference_end|>
@article{knill2024on,
    title={On Symmetries of Finite Geometries},
    author={Oliver Knill},
    journal={arXiv preprint arXiv:2408.13973},
    year={2024},
    archivePrefix={arXiv},
    eprint={2408.13973},
    primaryClass={nlin.SI cs.DM math-ph math.DS math.MP}
}