# The Trace of the affine Hecke category

@inproceedings{Gorsky2022TheTO, title={The Trace of the affine Hecke category}, author={Eugene Gorsky and Andrei Neguct}, year={2022} }

We compare the (horizontal) trace of the affine Hecke category with the elliptic Hall algebra, thus obtaining an “affine” version of the construction of [14]. Explicitly, we show that the aforementioned trace is generated by the objects Ed = Tr(Y d1 1 . . . Y dn n T1 . . . Tn−1) as d = (d1, . . . , dn) ∈ Z , where Yi denote the Wakimoto objects of [9] and Ti denote Rouquier complexes. We compute certain categorical commutators between the Ed’s and show that they match the categorical…

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