Type: Seminar

Distribution: World

Expiry: 1 Nov 2019

CalTitle1: Ciappara: Combinatorial actions of Soergel bimodules, Part I

Calendar2: 1 Nov 2019 1430-1630

CalLoc2: Quad S225

CalTitle2: Ciappara: Combinatorial actions of Soergel bimodules, Part II

Auth: romanova@10.17.126.181 (arom8272) in SMS-SAML

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.