Algebraic representation theory is a cross-disciplinary area of mathematics that in particular aims at making abstract algebraic objects accessible to combinatorial and computational methods, while at the same time trying to find and to use deeper categorical and homological structures. We are working on representations of finite and of algebraic groups, of Lie algebras and of associative algebras. Some of our typical topics are ranging from symmetric groups and other finite groups of Lie type over classical groups, Brauer algebras and Schur algebras to Auslander Reiten theory, cohomology and homological algebra as well as derived and triangulated categories. Connections to geometry, topology, mathematical physics and in particular number theory are studied for instance in the context of non-commutative geometry, categories of sheaves, quantum algebras, poynomial functors, integral representation theory and affine Hecke algebras.
There are strong connections and synergies among the different groups at IAZ and with other mathematicians in Stuttgart, in particular at IGT, as well as a wide range of national and international connections.
To learn more about our current research interests you may want to attend our research seminar or to browse the webpages of the members of IAZ.