Blocks of symmetric groups, semicuspidal KLR algebras and zigzag Schur-Weyl duality
Blocks of symmetric groups, semicuspidal KLR algebras and zigzag Schur-Weyl duality
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DOI：
10.4007/annals.2018.188.2.2
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发表时间：
2016-03
影响因子：
4.9
通讯作者：
A. Evseev;A. Kleshchev
中科院分区：
文献类型：
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作者：
A. Evseev;A. Kleshchev
我们证明了Turner猜想，该猜想将对称群的Hecke代数的块描述为某些显式Turner重代数，直到导出等价。Turner对偶是类Schur-代数的“局部”对象，在Brou-e-交换亏群猜想的背景下，取代了具有非交换亏群的对称群块的Brauer树代数的圈积.证明中使用的主要工具是对应于Z字形代数的圈积的广义Schur代数和仿射KLR代数的虚半角商.
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 Brou\'e 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.