DFF | Natural Sciences has supported Professor Henning Haahr Andersens project Representations of Algebraic Groups and Quantum Groups with 6,48 million DKK over a period of four years (starting date 01-07-2016).
About the project
An exciting new development occurred in modular representation theory two years ago when G. Williamson presented a sequence of counterexamples to Lusztig's conjecture on irreducible characters for semisimple algebraic groups. Until then it was universally believed that the conjecture would hold for all but small primes. In fact the PI behind this project had shown in joint work with J.C. Jantzen and W. Soergel that the conjecture always holds for very large primes. As a consequence of this development the research in the area has had to refocus. We need to find a new conjecture for these irreducible characters and the project will investigate the many questions raised in this process. In particular, we will explore the use of tilting modules, the relations to quantum groups, categorification methods, diagrammatics, and the more geometric approach using Demazure descent and derived categories.
An integrated part in the project is the education of young researchers in the field.