## Lie Groups and Representation Theory

Date, time & place Tuesday 16:30 - 18:00 126Room #126 (Graduate School of Math. Sci. Bldg.)

### 2015/05/19

17:00-18:30   Room #122 (Graduate School of Math. Sci. Bldg.)
Anton Evseev (University of Birmingham)
RoCK blocks, wreath products and KLR algebras (English)
[ Abstract ]
The so-called RoCK (or Rouquier) blocks play an important role in representation theory of symmetric groups over a finite field of characteristic $p$, as well as of Hecke algebras at roots of unity. Turner has conjectured that a certain idempotent truncation of a RoCK block is Morita equivalent to the principal block $B_0$ of the wreath product $S_p\wr S_d$ of symmetric groups, where $d$ is the "weight" of the block. The talk will outline a proof of this conjecture, which generalizes a result of Chuang-Kessar proved for $d < p$. The proof uses an isomorphism between a Hecke algebra at a root of unity and a cyclotomic Khovanov-Lauda-Rouquier algebra, the resulting grading on the Hecke algebra and the ideas behind a construction of R-matrices for modules over KLR algebras due to Kang-Kashiwara-Kim.