University of Sydney Algebra Seminar

Len Scott (University of Virginia)

Friday 20 March, 2:30-3:30pm, Place: Carslaw 275

From Forced Gradings to Q-Koszul algebras

This lecture is based on joint work with Brian Parshall. I want to tell a story about a new model for representation theory of semisimple algebraic groups, one involving "forcing" positive gradings on finite-dimensional algebras (sometimes called "generalized Schur algebras") that control their representation theory. This involves, at first, fairly familiar constructions arising from radical series filtrations, but later there is a more sophisticated construction, involving descent from radical series in algebras associated to quantum groups. Several applications and conjectures state properties which do not involve gradings at all. In the background is the new notion of Q-Koszul algebra, which is a structure similar to a Koszul algebra, but a candidate for structures modeling (at least "forced graded" version of) all Schur algebras, and most generalized Schur algebras.