Faisceaux caract\`eres sur les espaces de lacets d'alg\`ebres de Lie

We establish several foundational results regarding the Grothendieck-Springer affine fibration. More precisely, we prove some constructibility results on the affine Grothendieck-Springer sheaf and its coinvariants, enrich it with a group of symmetries, analog to the situation of Hitchin fibration, prove some perversity statements once we take some derived coinvariants and construct some specialization morphisms for the homology of affine Springer fibers. Along the way, we prove some homotopy result on l-adic complexes that can also be applied to Hitchin fibration.