We compare the canonical bases of level- quantised Fock spaces in affine types and , showing how to derive the canonical basis in type from the the canonical basis in type 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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Keywords: Quantum group, Fock space, symmetric groups, double covers, RoCK blocks
Fayers, Matthew 1
@article{ALCO_2023__6_5_1347_0, author = {Fayers, Matthew}, title = {Comparing {Fock} spaces in types $A^{(1)}$ and~$A^{(2)}$}, journal = {Algebraic Combinatorics}, pages = {1347--1381}, publisher = {The Combinatorics Consortium}, volume = {6}, number = {5}, year = {2023}, doi = {10.5802/alco.300}, language = {en}, url = {https://alco.centre-mersenne.org/articles/10.5802/alco.300/} }
TY - JOUR AU - Fayers, Matthew TI - Comparing Fock spaces in types $A^{(1)}$ and $A^{(2)}$ JO - Algebraic Combinatorics PY - 2023 SP - 1347 EP - 1381 VL - 6 IS - 5 PB - The Combinatorics Consortium UR - https://alco.centre-mersenne.org/articles/10.5802/alco.300/ DO - 10.5802/alco.300 LA - en ID - ALCO_2023__6_5_1347_0 ER -
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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