Evseev, Anton; Kleshchev, Alexander Blocks of symmetric groups, semicuspidal KLR algebras and zigzag Schur-Weyl duality. (English) Zbl 1435.20010 Ann. Math. (2) 188, No. 2, 453-512 (2018). Summary: 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. Cited in 3 ReviewsCited in 13 Documents MSC: 20C08 Hecke algebras and their representations 20C20 Modular representations and characters 20C30 Representations of finite symmetric groups 20G43 Schur and \(q\)-Schur algebras Keywords:blocks of symmetric groups; generalized Schur algebras; KLR algebras × Cite Format Result Cite Review PDF Full Text: DOI arXiv Link References: [1] Alperin, J. L., Weights for finite groups. The {A}rcata {C}onference on {R}epresentations of {F}inite {G}roups, Proc. Sympos. Pure Math., 47, 369-379, (1987) · Zbl 0657.20013 [2] Ariki, Susumu, On the decomposition numbers of the {H}ecke algebra of {\(G(m,1,n)\)}, J. Math. Kyoto Univ.. Journal of Mathematics of Kyoto Univ., 36, 789-808, (1996) · Zbl 0888.20011 · doi:10.1215/kjm/1250518452 [3] translated from the 2000 Japanese edition; revised by the author, Representations of Quantum Algebras and Combinatorics of {Y}oung Tableaux, Univ. 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