Bergeron-Legros, Gabriel2014-08-292014-08-2920142014http://hdl.handle.net/10393/31516http://dx.doi.org/10.20381/ruor-6345In this thesis, we present the Weil representation over loop symplectic groups. Then we study the question of whether or not the Schrodinger representation and the Weil representation are continuous. Finally, we define a cocycle of the rank 2 symplectic group, adapt Kubota's theorem to this case and verify that it splits over a subgroup.enKubotaWeilloop symplecticcocycleThesis