Blocks of symmetric groups, semicuspidal KLR algebras and zigzag Schur-Weyl 
duality

Evseev, Anton; Kleshchev, Alexander

doi:10.4007/annals.2018.188.2.2

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Blocks of symmetric groups, semicuspidal KLR algebras and zigzag Schur-Weyl duality

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Evseev, Anton
Max Planck Institute for Mathematics, Max Planck Society;

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Kleshchev, Alexander
Max Planck Institute for Mathematics, Max Planck Society;

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https://doi.org/10.4007/annals.2018.188.2.2
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arXiv:1603.03843.pdf
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Citation

Evseev, A., & Kleshchev, A. (2018). Blocks of symmetric groups, semicuspidal KLR algebras and zigzag Schur-Weyl duality. Annals of Mathematics, 188(2), 453-512. doi:10.4007/annals.2018.188.2.2.

Cite as: https://hdl.handle.net/21.11116/0000-0004-A7A5-5

Abstract

We prove Turner's conjecture, which describes the blocks of the Hecke algebras of the symmetric groups up to derived equivalence as certain explicit Turner double algebras. Turner doubles are Schur-algebra-like "local" objects,
which replace wreath products of Brauer tree algebras in the context of the Broué abelian defect group conjecture for blocks of symmetric groups with non-abelian defect groups. The main tools used in the proof are generalized Schur algebras corresponding to wreath products of zigzag algebras and
imaginary semicuspidal quotients of affine KLR algebras.