On Symmetries of Finite Geometries
Exactly Solvable and Integrable Systems
2024-09-04 v2 Discrete Mathematics
Mathematical Physics
Dynamical Systems
math.MP
Abstract
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.
Cite
@article{arxiv.2408.13973,
title = {On Symmetries of Finite Geometries},
author = {Oliver Knill},
journal= {arXiv preprint arXiv:2408.13973},
year = {2024}
}
Comments
10 pages, 2 figures, updated Mathematica code and additional graphics