SMS scnews item created by Anthony Henderson at Fri 16 Mar 2007 1802
Type: Seminar
Distribution: World
Expiry: 23 Mar 2007
Calendar1: 23 Mar 2007 1205-1255
CalLoc1: Carslaw 375
CalTitle1: Algebra Seminar: Mathas -- Classifying the blocks of the Ariki-Koike algebras
Auth: anthonyh@asti.maths.usyd.edu.au

Algebra Seminar

Classifying the blocks of the Ariki-Koike algebras

Andrew Mathas

23th March, 12:05-12:55pm, Carslaw 375


Abstract

In this talk I will explain the classification of the blocks of the Ariki-Koike algebras, which are certain finite dimensional quotients of the affine Hecke algebra of the general linear group. The key idea of the proof is not to work with the Ariki-Koike algebras at all and, instead, to classify the blocks of the cyclotomic Schur algebras. These latter algebras have the "same" blocks as the Ariki-Koike algebras and they have the added advantage that they are quasi-hereditary algebras. As a consequence, we can use a cute new trick with the Jantzen sum formula to reduce the classification of the blocks of the cyclotomic Schur algebras (and the Ariki-Koike algebras) to a purely combinatorial problem.

This is joint work with Sinéad Lyle.


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