Gaitsgory’s Central Sheaves via the Diagrammatic Hecke Category

We initiate the study of Gaitsgory’s central sheaves using complexes of Soergel bimodules, in extended affine type A A . We construct the complex associated to the standard representation, and prove that it lives in the Drinfeld center of the category. We conjecture that this complex can be flattened to a central complex in finite type A A , which is the complex sought after in a conjecture of Gorsky-Negut-Rasmussen. Along the way, we extend diagrammatic technology in several directions. We develop diagrammatics for Soergel bimodules for extended affine Weyl groups. We compute idempotents and describe a thick calculus for certain elements in affine Weyl groups.