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The goal of this work is to construct a perverse t-structure on theinfinity-category of l-adic LG-equivariant sheaves on the loop Lie algebra Lgand to show that the affine Grothendieck-Springer sheaf S is perverse.Moreover, S is an intermediate extension of its restriction to the locus of``compact" elements with regular semi-simple reduction. Note that classicalmethods do not apply in our situation because LG and Lg areinfinite-dimensional ind-schemes.

Perverse sheaves on infinite-dimensional stacks, and affine Springer theory