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We compare the canonical bases of level-$1$ quantised Fock spaces in affinetypes $A^{(1)}$ and $A^{(2)}$, showing how to derive the canonical basis intype $A^{(2)}_{2n}$ from the the canonical basis in type $A^{(1)}_n$ in certainweight spaces. In particular, we derive an explicit formula for the canonicalbasis in extremal weight spaces, which correspond to RoCK blocks of doublecovers of symmetric groups. In a forthcoming paper with Kleshchev and Morottiwe will use this formula to find the decomposition numbers for RoCK blocks ofdouble covers with abelian defect.

Comparing Fock spaces in types $A^{(1)}$ and $A^{(2)}$