The isotropic lines of Z_{d}^{2}

Details The isotropic lines of Z_{d}^{2} The isotropic lines of Z_{d}^{2}

2008-09-18

arxiv.org/abs/0809.3220v2

J. Phys. A: Math. Theor. 42 (2009) 072001

Physics

Mathematical Physics

10 pages

Scientific paper

10.1088/1751-8113/42/7/072001

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.

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