Introduction to Representation Theory
Georg Lehner
Additional information / Pre-requisites
Lineare Algebra I
Comments
If one has an object with symmetries, for example a polytope, or also a polynomial, one has a group - namely the group of symmetries of said object. The study of groups thus forms one of the most central topics in mathematics. A group can be studied by its action on such objects. We are going to study, in some sense, the easiest possible actions of finite groups: the linear actions on vector spaces. Such actions are called representations of finite groups. The study of such actions combines the methods of linear algebra with group theory, and has numerous applications in different areas of mathematics.
Preliminary program:
Generalities on linear representations, irreducible representations and operation on representations. Character theory, Schur’s lemma, decompositions of representations. Subgroups and induced representations. Explicit examples. Representations of the symmetric group.
closeSuggested reading
W. Fulton, J. Harris, Representation Theory - A First Course, GTM 129
13 Class schedule
Regular appointments