We prove that certain parabolic Kazhdan-Lusztig polynomials calculate the graded decomposition matrices of v-Schur algebras given by the Jantzen filtration of Weyl modules, confirming a conjecture of Leclerc and Thibon.

In this paper a proof of Conjecture 9.12 of Braverman–Kazhdan in their article γ-functions of representations and lifting on the acyclicity of their l-adic γ-sheaves over certain affine spaces is given for GL(n).