School of Mathematics and Statistics
Andrew Mathas
University of Sydney
Tilting modules for cyclotomic Schur algebras.
Friday August 3rd, 121pm,
Carslaw 375.
The cyclotomic Schur algebras are endomorphism algebras
of a direct sum of ``permutation like'' modules for the
ArikiKoike algebras: they include as special cases the
qSchur algebras of Dipper and James. These algebras
were introduced partly to provide a new tool for
studying the ArikiKoike algebras and partly in the
hope that they might generalize the beautiful
DipperJames theory which shows that the qSchur
algebras completely determine the modular
representation theory of the GL_{n}(q) in
nondefining 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 quasihereditary 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.
