The isotropic lines of Z_{d}^{2}
Mathematical Physics
2009-02-04 v2 math.MP
Quantum Physics
Abstract
We show that the isotropic lines in the lattice Z_{d}^{2} are the Lagrangian submodules of that lattice and we give their number together with the number of them through a given point of the lattice. The set of isotropic lines decompose into orbits under the action of SL(2,Z_d). We give an explicit description of those orbits as well as their number and their respective cardinalities. We also develop two group actions on the group \Sigma_{D}(M) related to the topic.
Cite
@article{arxiv.0809.3220,
title = {The isotropic lines of Z_{d}^{2}},
author = {Olivier Albouy},
journal= {arXiv preprint arXiv:0809.3220},
year = {2009}
}
Comments
10 pages