Hecke categories, idempotents, and commuting stacks

Abstract We formulate a connection between a topological and a geometric category. The former is the idempotent completion of the (horizontal) trace of the affine Hecke category, while the latter is the equivariant derived category of the (semi-nilpotent) commuting stack. This provides a more precise and improved version of our proposal in Gorsky and Neguț (Proc Lond Math Soc (3) 126(6): 2013–2056, 2023).