q-Analogues of regularisation theorems for linear and projective representations of the symmetric group

Brundan and Kleshchev have recently proved an analogue of Jamesʹs ‘regularisation theorem’ for modular representations of symmetric groups, in the context of projective representations. We prove ‘q-analogues’ of both theorems, i.e. corresponding theorems concerning canonical basis coefficients for basic representations of quantum affine algebras of types and .