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

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.
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Contributor : Olivier Albouy <>
Submitted on : Wednesday, January 7, 2009 - 1:56:11 PM
Last modification on : Tuesday, November 19, 2019 - 2:37:59 AM
Long-term archiving on: : Wednesday, September 22, 2010 - 11:21:33 AM

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O. Albouy. The isotropic lines of Z_{d}^{2}. Journal of Physics A: Mathematical and Theoretical, IOP Publishing, 2009, 42, pp.072001. ⟨10.1088/1751-8113/42/7/072001⟩. ⟨in2p3-00322707v2⟩

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