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Abstract We compare the (horizontal) trace of the affine Hecke category with the elliptic Hall algebra, thus obtaining an “affine” version of the construction of Gorsky et al. (Int. Math. Res. Not. IMRN2022(2022) 11304–11400). Explicitly, we show that the aforementioned trace is generated by the objects as , where denote the Wakimoto objects of Elias and denote Rouquier complexes. We compute certain categorical commutators between the 's and show that they match the categorical commutators between the sheaves on the flag commuting stack that were considered in Neguț (Publ. Math. Inst. Hautes Études Sci. 135 (2022) 337–418). At the level of ‐theory, these commutators yield a certain integral form of the elliptic Hall algebra, which we can thus map to the ‐theory of the trace of the affine Hecke category.
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This content will become publicly available on September 15, 2026
Super Caldero–Chapoton map for type A
One can explicitly compute the generators of a surface cluster algebra either combinatorially, through dimer covers of snake graphs, or homologically, through the CC-map applied to indecomposable modules over the appropriate algebra. Recent work by Musiker, Ovenhouse and Zhang used Penner and Zeitlin's decorated super Teichmüller theory to define a super version of the cluster algebra of type A and gave a combinatorial formula to compute the even generators. We extend this theory by giving a homological way of explicitly computing these generators by defining a super CC-map for type A.
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- Award ID(s):
- 2054255
- PAR ID:
- 10641402
- Publisher / Repository:
- Elsevier
- Date Published:
- Journal Name:
- Journal of Algebra
- ISSN:
- 0021-8693
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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