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).
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