University of Sydney
School of Mathematics and Statistics
Andrew Mathas
University of Sydney
Tilting modules for cyclotomic Schur algebras.
Friday August 3rd, 12-1pm,
Carslaw 375.
The cyclotomic Schur algebras are endomorphism algebras
of a direct sum of ``permutation like'' modules for the
Ariki-Koike algebras: they include as special cases the
q-Schur algebras of Dipper and James. These algebras
were introduced partly to provide a new tool for
studying the Ariki-Koike algebras and partly in the
hope that they might generalize the beautiful
Dipper-James theory which shows that the q-Schur
algebras completely determine the modular
representation theory of the GLn(q) in
non-defining characteristic.
As yet there are no known (non type A) connections
between the representation theory of the cyclotomic
Schur algebras and that of the finite groups of Lie
type; nonetheless the representation theory of these
algebras is both rich and beautiful. For example, they
are quasi-hereditary algebras and Jantzen's sum formula
generalizes to this setting. In this talk I will survey
the representation theory of the cyclotomic Schur
algebras culminating with a description of their
tilting modules.
|