Comparing Fock spaces in types A (1) and A (2)

Abstract

We compare the canonical bases of level-1 quantised Fock spaces in affine types A (1) and A (2) , showing how to derive the canonical basis in type A 2n (2) from the the canonical basis in type A n (1) in certain weight spaces. In particular, we derive an explicit formula for the canonical basis in extremal weight spaces, which correspond to RoCK blocks of double covers of symmetric groups. In a forthcoming paper with Kleshchev and Morotti we will use this formula to find the decomposition numbers for RoCK blocks of double covers with abelian defect.