Equating decomposition numbers for different primes

This paper shows that certain decomposition numbers for the Iwahori–Hecke algebras of the symmetric groups and the q-Schur algebras at different roots of unity in characteristic zero are equal. To prove our results we first establish the corresponding theorem for the canonical basis of the level-one Fock space and then apply deep results of Ariki and Varagnolo–Vasserot.