Detailseite
Projekt
Combinatorial and geometric structures for reflection groups and groupoids
Antragsteller
Professor Dr. Michael Cuntz; Professor Dr. Christian Stump
Fachliche Zuordnung
Mathematik
Förderung
Förderung von 2013 bis 2017
Projektkennung
Deutsche Forschungsgemeinschaft (DFG) - Projektnummer 239354514
There are numerous combinatorial and geometric structures related to finite Weyl groups that are studied in various fields of mathematics. Particular examples are noncrossing partitions, Shi arrangements, cluster algebras, subword complexes, root posets, and q; t-Catalan numbers. These structures are deeply related and each of them reflects certain properties of the finite Weyl groups. There are several very natural generalizations of finite Weyl groups: A fine Weyl groups, Coxeter groups, complex reflection groups, Weyl groupoids, and simplicial arrangements. Each of these generalizations maintains some of the properties of the finite Weyl group and thus retains some of the combinatorics. For two reasons, there are many pieces missing to the big picture of reflection structures. On the one hand, some of the combinatorial structures have been introduced just recently. On the other hand, some of the generalizations are new or have experienced a renaissance in the last years. We propose to fill the gaps by implementing a package for reflection structures for Sage and GAP, and by then using it to collect experimental evidence for new conjectures and eventually to help us prove new theorems.
DFG-Verfahren
Schwerpunktprogramme
