Appears in collection : Arithmetic and Algebraic Geometry: A conference in honor of Ofer Gabber on the occasion of his 60th birthday

This is a joint work with A. Bouthier and D. Kazhdan.Let G be a connected reductive group, and let LG be the corresponding loop group. Our main goal is to construct a "perverse" t-structure on the derived category of Ad LG-equivariant sheaves on LG and to show that the affine Grothendieck-Springer sheaf belongs to its core.More precisely, we construct the t-structure on the derived category of LG-equivariant sheaves supported on bounded regular semi-simple elements of LG, and we only consider its Lie algebra analog.