Grading the translation functors in type A

We deal with the representation theory of quantum groups and Hecke algebras at roots of unity. We relate the philosophy of Andersen, Jantzen and Soergel on graded translated functors to the Lascoux, Leclerc and Thibon algorithm. This goes via the Murphy standard basis theory and the idempotents coming from the Murphy–Jucys operators. Our results lead to a guess on a tilting algorithm outside the lowest p2 alcove, which at least in the SL2-case coincides with Erdmannʹs results.