Graded cellularity and the monotonicity conjecture

Abstract

The graded cellularity of Libedinsky double leaves, which form a basis for the endomorphism ring of the Bott–Samelson–Soergel bimodules, allows us to view the Kazhdan–Lusztig polynomials as graded decomposition numbers. Using this interpretation, we can provide a proof of the monotonicity conjecture for any Coxeter system.