Lie algebras A non-perverse Soergel bimodule in type A Un bimodule de Soergel non pervers de type A (original) (raw)

Article history: Received 21 July 2017 Accepted 25 July 2017 Available online 7 August 2017 Presented by Michèle Vergne A basic question concerning indecomposable Soergel bimodules is to understand their endomorphism rings. In characteristic zero all degree-zero endomorphisms are isomorphisms (a fact proved by Elias and the second author) which implies the Kazhdan–Lusztig conjectures. More recently, many examples in positive characteristic have been discovered with larger degree zero endomorphisms. These give counter-examples to expected bounds in Lusztig’s conjecture. Here we prove the existence of indecomposable Soergel bimodules in type A having non-zero endomorphisms of negative degree. This gives the existence of a non-perverse parity sheaf in type A. © 2017 Académie des sciences. Published by Elsevier Masson SAS. All rights reserved.