Physical & Biological Sciences Division
Professor
Faculty
McHenry Library
McHenry Building Room #4190
Mathematics Department
Professor of Mathematics
Dr. rer. nat. habil., University of Augsburg 1995
Ph.D., University of Augsburg 1989
Robert Boltje and his students work in the representation theory of finite groups. They are primarily involved with the conjectures of Alperin, Broué and Dade. Current research interests include canonical induction formulas, biset functors, fusion systems, block theory of group algebras, and equivalences between such blocks. Professor Boltje has also worked in the area of algebraic number theory, where he has developed functorial methods to understand Galois actions on rings of algebraic integers, and other structures associated to number fields.
Robert Boltje’s research centers around the theory of finite groups, their representations, and applications to algebraic number theory. Within the theory of finite group representations he has been working on natural induction formulae for many years. A very useful tool in this theory is the language of Mackey functors and biset functors. This structure occurs surprisingly often in different fields of mathematics when group actions on mathematical objects (sets, vector spaces, topological spaces, fibre bundles) are present. Also, the presence of a Mackey functor structure on the ideal class groups of number fields in a fixed Galois extension provides relations between these class groups. The ideal class group is an invariant which measures how close the ring of integers in a number field is to having unique factorization into primes.
Presently, Robert Boltje is interested in the conjectures of Alperin, Dade, and Broué in the representation theory of finite groups. These conjectures link blocks of representations of a finite group G to blocks of representations of various subgroups arising as normalizers of chains of p-subgroups of G. It seems that the topology of the simplicial complex of p-subgroups together with its G-action plays an important role, and that ideas from other fields of mathematics like geometry or algebraic topology might help to prove the conjectures.
- R. Boltje: A general theory of canonical induction formulae, J. Algebra (1998), 293-343.
- R. Boltje: Linear source modules and trivial source modules, Proc. Sympos. Pur Math. 63 (1998), 7-30.
- R. Boltje: Class groups relations from Burnside ring idempotents, J. Number Theory (66)(1997),291-305
- R. Boltje: Identities in representation theory via chain complexes, J. Algebra 167 (1994), 417-447.
- R. Boltje: A canonical Brauer induction formula, Astérisque 181-182 (1990), 31-59.
