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arXiv · 0809.3220

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

Olivier Albouy
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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 Σ_{D}(M) related to the topic.

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Olivier Albouy. 2009-01-07. The isotropic lines of Z_{d}^{2}. https://doi.org/10.1088/1751-8113%2F42%2F7%2F072001

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