RoCK blocks, wreath products and KLR algebras
Abstract
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 weight $d$ of a symmetric group $\mathfrak S_n$ defined over a field $F$ of characteristic $e$ is Morita equivalent to the principal block of the wreath product $\mathfrak S_e \wr \mathfrak S_d$. This generalises a theorem of Chuang and Kessar that applies to RoCK blocks with abelian defect groups. Our proof relies crucially on an isomorphism between $F\mathfrak S_n$ and 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.
- Publication:
-
arXiv e-prints
- Pub Date:
- November 2015
- DOI:
- 10.48550/arXiv.1511.08004
- arXiv:
- arXiv:1511.08004
- Bibcode:
- 2015arXiv151108004E
- Keywords:
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- Mathematics - Representation Theory;
- 20C08;
- 20C30
- E-Print:
- Version 2: minor revisions and corrections. To appear in Math. Annalen