Journal of Algebra 320 (2008) 2675-2694.

I introduce the light leaves basis, a basis of the Hom space between Soergel bimodules. They have been useful in the disproof of Lusztig  and James conjectures,  in the algebraic proof of KL conjecture, in the  proof of the positivity of the coefficients of KL polynomials (and its parabolic version), in the algebraic proof of Jantzen conjecture, and in many other contexts. It has also been a key ingredient to the new approach to modular representation theory by Williamson and Riche.

PDF Sur la catégorie des bimodules de Soergel