Geodesic
Blocks of symmetric groups, semicuspidal KLR algebras and zigzag Schur-Weyl duality
Anton Evseev1 ; Alexander Kleshchev2
1 University of Birmingham, Birmingham, UK
2 University of Oregon, Eugene OR
Annals of mathematics, Tome 188 (2018) no. 2, pp. 453-512

Voir la notice de l'article provenant de la source Annals of Mathematics website

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.

DOI : 10.4007/annals.2018.188.2.2

Anton Evseev 1 ; Alexander Kleshchev 2

1 University of Birmingham, Birmingham, UK
2 University of Oregon, Eugene OR 
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Anton Evseev; Alexander Kleshchev. Blocks of symmetric groups, semicuspidal KLR algebras and zigzag Schur-Weyl duality. Annals of mathematics, Tome 188 (2018) no. 2, pp. 453-512. doi: 10.4007/annals.2018.188.2.2

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