Type: Seminar

Distribution: World

Expiry: 6 Apr 2020

CalTitle1: Algebra Seminar: Perversity of categorical braid group actions

Auth: kevinc@pkevinc.pc (assumed)

Oded Yacobi (University of Sydney) Friday 13 March, 12-1pm, Place: Carslaw 275 Title: Perversity of categorical braid group actions Abstract: Let g be a semisimple Lie algebra with simple roots I, and let C be a category endowed with a categorical g-action. Recall that Chuang-Rouquier construct, for every i in I, the Rickard complex acting as an autoequivalence of the derived category D^b(C), and Cautis-Kamnitzer show these define an action of the braid group B_g. As part of an ongoing project with Halacheva, Licata, and Losev we show that the positive lift to B_g of the longest Weyl group element acts as a perverse auto-equivalence of D^b(C). (This generalises a theorem of Chuang-Rouquier who proved it for g = sl(2).) This implies, for instance, that for a minimal categorification this functor is t-exact (up to a shift). Perversity also allows us to "crystallise" the braid group action, to obtain a cactus group action on the set of irreducible objects in C. This agrees with the cactus group action arising from the g-crystal (due to Halacheva-Kamnitzer-Rybnikov-Weekes). Note: This is the same talk I recently gave at the meeting in Mooloolaba.