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

Fayers, Matthew

doi:10.5802/alco.300

Geodesic

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Comparing Fock spaces in types

A^{(1)}

and

A^{(2)}

Fayers, Matthew ¹

¹ Queen Mary University of London Mile End Road London E1 4NS U.K.

Algebraic Combinatorics, Tome 6 (2023) no. 5, pp. 1347-1381

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Résumé

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 $A_{2 n}^{(2)}$ 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.

Reçu le : 2022-08-09
Accepté le : 2023-01-31
Publié le : 2023-11-07

DOI : 10.5802/alco.300

Classification : 17B37, 05E10, 20C25, 20C30
Keywords: Quantum group, Fock space, symmetric groups, double covers, RoCK blocks

Affiliations des auteurs :

Fayers, Matthew ¹

¹ Queen Mary University of London Mile End Road London E1 4NS U.K.

Licence :

CC-BY 4.0

Droits d'auteur : Les auteurs conservent leurs droits

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Fayers, Matthew. Comparing Fock spaces in types $A^{(1)}$ and $A^{(2)}$. Algebraic Combinatorics, Tome 6 (2023) no. 5, pp. 1347-1381. doi: 10.5802/alco.300

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