
## 4. Soergel bimodules

1. #### Problem 4.1.

What is the Drinfeld center of K$^b(\mathbb{S}\text{Bim}_{\text{fin}})$? K$^b(\mathbb{S}\text{Bim}_{\text{aff}})$? Are there additional complexes in K$^b(\mathbb{S}\text{Bim})$ which commute with $\mathbb{S}$Bim?
• #### Problem 4.2.

Is Z(K$^b(\mathbb{S}\text{Bim}_{\text{ext}})$) generated by Gaitsgory central sheaves? Is Z(K$^b(\mathbb{S}\text{Bim}_{\text{fin}}))$ generated by images of Gaitsgory central sheaves? Is Z(K$^b(\mathbb{S}\text{Bim}_{\text{fin}}))$ split generated by powers of FT$_n$? Is Z(K$^b(\mathbb{S}\text{Bim}_{\text{fin}}))$ symmetric monoidal?
• #### Problem 4.3.

Is the flattening of the Gaitsgory complex for the standard representation equal to the tautological sheaf from the GNR conjecture?

Cite this as: AimPL: Categorified Hecke algebras, link homology, and Hilbert schemes, available at http://aimpl.org/catheckehilbert.