Аннотация
Using a geometric argument building on our new theory of graded sheaves, we
compute the categorical trace and Drinfel'd center of the (graded) finite Hecke
category $H_W^gr = Ch^b(SBim_W)$ in terms
of the category of (graded) unipotent character sheaves, upgrading results of
Ben-Zvi-Nadler and Bezrukavninov-Finkelberg-Ostrik. In type $A$, we relate the
categorical trace to the category of $2$-periodic coherent sheaves on the
Hilbert schemes $Hilb_n(C^2)$ of points on $C^2$
(equivariant with respect to the natural $C^* C^*$
action), yielding a proof of a conjecture of Gorsky-Negut-Rasmussen which
relates HOMFLY-PT link homology and the spaces of global sections of certain
coherent sheaves on $Hilb_n(C^2)$. As an important
computational input, we also establish a conjecture of Gorsky-Hogancamp-Wedrich
on the formality of the Hochschild homology of $H_W^gr$.
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