Algebra Seminar

One of the landmark problems of twentieth-century mathematics was to calculate the character table of a reductive group over a finite field. Green's combinatorial solution in 1955 of the case of the general linear groups proved very difficult to generalize. The breakthrough was made by Lusztig (partly in collaboration with Deligne) in the 70s and 80s, using geometrical methods such as intersection cohomology. I'll give a brief introduction to Lusztig's theory of character sheaves, and also discuss its application to a related problem, where a combinatorial approach is unknown even for the general linear groups.