Algebra Seminar: Evseev -- Turner doubles and RoCK blocks of symmetric groups

Anton Evseev (Universty of Birmingham)

Friday 4 March, 12-1pm, Place: Carslaw 375

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 Sd. 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.