Research Projects of Prof. Bessenrodt
Symmetry is a basic concept in geometry, and in a much deeper sense symmetries are fundamental to many structures in mathematics and physics and lead to important invariants. The mathematical study of symmetries is at the heart of the theory of groups, algebras and their representations; there is often also a close relationship to combinatorics and the theory of symmetric functions. These are the main research areas of the algebra group.
The research of Professor Christine Bessenrodt is concerned with the representation theory of finite groups and algebraic combinatorics. A main focus is on the symmetric groups (and closely related groups and algebras), the combinatorics of partitions and tableaux, Schur functions and their generalisations, and the fruitful interplay between these topics.
For the representation theory of finite groups, the simple groups play an important special role; based on their classification, a strategy for proving results on general finite groups is to reduce such problems to the simple (or quasisimple) groups and prove the assertions for these groups. One of the few infinite families of finite simple groups is the series of alternating groups whose representation theory is intricately interwoven with that of the symmetric groups; this provides a special motivation for studying these groups. The numerous connections to other areas such as invariant theory, algebraic geometry, Lie theory, stochastics and applications in physics has led to very active research worldwide in the past decades.
Our work contributes both to the character theory as well as to the modular representation theory of finite groups, in particular providing new information on blocks and their invariants and the decomposition of tensor products; our study of different types of Schur functions is closely connected to the combinatorics of Kronecker and Littlewood-Richardson coefficients.