Finite dimensional Hecke algebras

Details Finite dimensional Hecke algebras Finite dimensional Hecke algebras

2007-08-03

arxiv.org/abs/0708.0446v4

Mathematics

Representation Theory

40 pages,(v2,v3) some minor errors corrected (v4) several more corrections, references added

Scientific paper

These are notes prepared for ICRA workshop at Torun, Poland, August 2007. In the first part, we explain results on canonical basic sets by Geck and Jacon and propose a categorification framework which is suitable for our example of Hecke algebras. In the second part, we review basics of Kashiwara crystal and explain the Fock space theory of cyclotomic Hecke algebras and its applications. In the third part, we explain Rouquier's theory of quasihereditary covers of cyclotomic Hecke algebras. We add detailed explanation of the proofs here. The third part is based on my intensive course given at Nagoya university in January 2007.

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