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

Anton Evseev, Alexander Kleshchev

Research output: Contribution to journalArticlepeer-review

5 Citations (Scopus)
112 Downloads (Pure)

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.
Original languageEnglish
Pages (from-to)453-512
Number of pages60
JournalAnnals of Mathematics
Volume188
Issue number2
DOIs
Publication statusPublished - 1 Sep 2018

Keywords

  • blocks of symmetric groups
  • generalized Schur algebras
  • KLR algrbras

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