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

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.