  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.

Algebraic Geometry;Group Theory;Representation Theory