Faisceaux caractères sur les espaces de lacets d'algèbres de Lie

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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.We enrich it with a group of symmetries, analogously to the situation of Hitchin fibration.We prove some perversity statements once we take some derived coinvariants, and we construct some specialization morphisms for the homology of affine Springer fibers.