# Anton Evseev (Universty of Birmingham)

## Turner doubles and RoCK blocks of symmetric groups.

The so-called RoCK blocks play an important role in representation theory of symmetric groups and Hecke algebras at roots of unity. RoCK blocks have a much simpler structure than general blocks of Hecke algebras. W. Turner conjectured that every RoCK block of weight $$d$$ is Morita equivalent to a double’ algebra, which is a local’ Schur-algebra-like object related to the wreath product of a Brauer tree algebra with the symmetric group $$S_d$$. The talk will outline a proof of this conjecture, which uses Khovanov-Lauda-Rouquier algebras in an essential way. The result implies that every block of a Hecke algebra of the symmetric group is derived equivalent to the appropriate Turner double. During the talk, I will aim to give an overview of the construction of KLR algebras and that of Turner doubles. The talk is based on joint work with Alexander Kleshchev.