Informal Friday Seminar: Ciappara -- Combinatorial actions of Soergel bimodules

Let G be an algebraic group, connected, simply connected, and semisimple over an
algebraically closed field of characteristic p > 0.  This two-part talk will span
classical "independence of p" results due to Andersen-Jantzen-Soergel (AJS) and
recent work of Abe towards constructing a Hecke category action on Rep_0(G).  

In Part I, we will survey the landscape in which AJS (Asterisque, 1994) was situated,
before looking in detail at their constructions and methods of proof.  A key takeaway
will be their introduction of combinatorial categories generalising G_1 T-modules, which
admit translation functors, a linkage principle, and so on.  If time permits, we will
discuss related work of Fiebig (2007), which will be useful the following week.  

In Part II, we will discuss ideas from two papers of Abe (2019), who has described a new
realisation of the category of Soergel bimodules and an action on the principal block of
G_1 T-modules through the combinatorics of AJS.