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_{w}, 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 B_{0} 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

# Graded RoCK blocks and wreath products

Speaker:

Anton Evseev (Birmingham)

Date/Time:

Mon, 20/10/2014 - 18:00

Room:

103

Seminar series: