RoCK blocks, wreath products and KLR algebras
RoCK blocks, wreath products and KLR algebras
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DOI：
10.1007/s00208-016-1493-z
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发表时间：
2015-11
影响因子：
1.4
通讯作者：
A. Evseev
中科院分区：
文献类型：
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作者：
A. Evseev
我们考虑对称群和Hecke代数在单位根上的RoCK（或Rouquier）块。本文证明了Turner的一个猜想，即定义在特征域F上的对称群的权为d的RoCK块的幂等截断是Morita等价于圈积的主块。这推广了Chuang和Kessar的一个定理，该定理适用于具有阿贝尔亏损群的RoCK块。我们的证明依赖于一个同构和分圆Khovanov-Lauda-Rouquier代数，和森田等价，我们生产的是分次代数。我们还证明了类似的结果岩堀-Hecke代数在一个根的单位定义在任意域上。
We consider RoCK (or Rouquier) blocks of symmetric groups and Hecke algebras at roots of unity. We prove a conjecture of Turner asserting that a certain idempotent truncation of a RoCK block of weightdof a symmetric groupdefined over a fieldFof characteristiceis Morita equivalent to the principal block of the wreath product. This generalises a theorem of Chuang and Kessar that applies to RoCK blocks with abelian defect groups. Our proof relies crucially on an isomorphism betweenand a cyclotomic Khovanov–Lauda–Rouquier algebra, and the Morita equivalence we produce is that of graded algebras. We also prove the analogous result for an Iwahori–Hecke algebra at a root of unity defined over an arbitrary field.