Repræsentationsteori
4 hours of lectures per week
Lecturer Jens Carsten Jantzen Content This will be an introduction to a large field of modern mathematics. At first we shall look at representations of finite groups, mainly over the field of complex numbers. In this case representations are determined by their characters (certain functions on the group) and we shall get to knowmethods how to compute these functions. Induced representations will be discussed. As an application, Burnside's theorem (a finite group is solvable if its order is a product of two prime powers) will be proved.
We shall then look more deeply into the representation theory of the symmetric groups. There is a close connection between their representations and those of the general linear groups that we shall use to go beyond the region of finite groups and to get into certain infinite groups.
Prerequisites Algebra 1.
Literature G. D. James, M. W. Liebeck:
Representations and Characters of Groups, 2nd edition, Cambridge University Press, 2001.
-to be supplemented by notes.