The modular representation theory of reductive algebraic groups (general linear groups being an example of such groups) has a number of longstanding open problems. Several of these problems have conjectured resolutions that involve special modules known as indecomposable tilting modules. In this talk we will look at how tilting modules relate to two problems in particular:
- lifting representations from the Lie algebra to the algebraic group, and
- finding a character formula for the irreducible representations.
A good deal of background material will be provided throughout.
This video is part of the University of Georgia‘s Algebra seminar.
