Algebra Seminar: Len Scott -- From Forced Gradings to Q-Koszul algebras

This lecture is based on joint work with Brian Parshall.cI want to tell a story about a
new model forcrepresentation theory of semisimple algebraic groups, one
involvingc“forcing” positive gradings on finite-dimensional algebras (sometimes
calledc“generalized Schur algebras’’) that control their representation theory.cThis
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 a Q-Koszul algebra, which is a structure similar to a Koszul algebra,
but a candidate for structures modeling (at least “forced graded” versions of) all Schur
algebras, and most generalized Schur algebras.