Comparing Fock spaces in types A (1) and A (2)
Algebraic Combinatorics, Volume 6 (2023) no. 5, pp. 1347-1381.

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.

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DOI: 10.5802/alco.300
Classification: 17B37, 05E10, 20C25, 20C30
Keywords: Quantum group, Fock space, symmetric groups, double covers, RoCK blocks

Fayers, Matthew 1

1 Queen Mary University of London Mile End Road London E1 4NS U.K.
License: CC-BY 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights
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Fayers, Matthew. Comparing Fock spaces in types $A^{(1)}$ and $A^{(2)}$. Algebraic Combinatorics, Volume 6 (2023) no. 5, pp. 1347-1381. doi : 10.5802/alco.300. https://alco.centre-mersenne.org/articles/10.5802/alco.300/

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