School of Mathematical Sciences

Graded RoCK blocks and wreath products menu

Graded RoCK blocks and wreath products

Speaker: 
Anton Evseev (Birmingham)
Date/Time: 
Mon, 20/10/2014 - 18:00
Room: 
103
Seminar series: 

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 B0 of the wreath product Spwr Sw, where w is the "weight" of the block. More precisely (and more simply), the conjecture states that the idempotent truncation in question is isomorphic to a tensor product of B0 and a certain matrix algebra. The talk will outline a proof of this conjecture, which uses an isomorphism between the group algebra of a symmetric group and a cyclotomic Khovanov-Lauda-Rouquier algebra and the resulting grading on the group algebra of the symmetric group. This result generalizes a theorem of Chuang-Kessar, which applies to the case w