Joint with Geordie Williamson, Proc. London. Math. Soc. 109 (2014), no. 5, 1264-1280.
For any Coxeter system, we establish the existence of analogues of standard and costandard objects in 2-braid groups, thus proving a conjecture that Rouquier stated in the ICM 2006. This result was a key step for the proof by Elias and Williamson of Kazhdan-Lusztig conjectures