Perversity of coinvariants of affine Springer sheaves

TL;DR

This paper develops a new perverse t-structure on certain sheaves related to affine Springer theory and proves that derived coinvariants of affine Grothendieck--Springer sheaves are perverse, advancing geometric representation theory.

Contribution

It introduces a novel perverse t-structure on LG-equivariant sheaves and proves the perversity of derived coinvariants, utilizing Yun's compatibility theorem.

Findings

Derived τ-coinvariants of affine Springer sheaves are perverse

Constructed a new perverse t-structure on LG-equivariant sheaves

Proved compatibility of actions using Yun's theorem

Abstract

Using techniques of [BKV], we construct a perverse t-structure on the infinity-category of l-adic LG-equivariant sheaves on the regular-semisimple bounded locus of the loop group LG and prove that the derived $\tau$-coinvariants of affine Grothendieck--Springer sheaves are perverse. Our main new ingredient is a theorem of Yun on compatibility of actions.