Multiplicity Free Actions

• Applicant: Professor Dr. Friedrich Knop
• Subject Area: Mathematics
• Term: from 2009 to 2015
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 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 Programme: Priority Programmes
• Subproject of: SPP 1388: Representation Theory