Multiplicity Free Actions

• Antragsteller: Professor Dr. Friedrich Knop
• Fachliche Zuordnung: Mathematik
• Förderung: Förderung von 2009 bis 2015
• Projektkennung: Deutsche Forschungsgemeinschaft (DFG) - Projektnummer 124928714

In this project we study spaces, called spherical varieties, which have in a precise sense the highest possible degree of symmetry. They are generalizations of the round 2-sphere. In the first phase we have completed their classification, explained their relationship with new combinatorial structures, and studied some of their geometric properties. We also worked on related issues about multiplicity free Hamiltonian manifolds. In this continuation, we plan to apply this new insight to obtain further developments in the study of spherical varieties and, more in general, to algebraic group actions. Among these applications are the study of orbits and orbit closures in algebraic varieties and representation spaces, of orbits of a Borel subgroup, and further research on spherical functions, which are generalizations of spherical harmonics on the 2-sphere. In addition, generalizations of this theory to positive characteristic and to infinite-dimensional algebraic groups are planned.

• DFG-Verfahren: Schwerpunktprogramme
• Teilprojekt zu: SPP 1388: Representation Theory (Darstellungstheorie)