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\(\newcommand{\Cat}{{\rm Cat}} \) \(\newcommand{\A}{\mathcal A} \) \(\newcommand{\freestar}{ \framebox[7pt]{$\star$} }\)

4. Soergel bimodules


    1. Add remark

      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?


        • Add remark

          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?


            • Add remark

              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.