Symplectic Structures in Geometry, Algebra and Dynamics
Collaborative Research Centre TRR 191
A1, A2, A3, A5, A6, A7, A8
B1, B2, B3, B4, B5, B6, B7, B8
C1, C2, C3, C4, C5, C6, C7
Dynamics & Variational Methods
B4: Loop groups and the path model
(completed in the first funding period 2017-2020)
The project intends to give a geometric reinterpretation of the combinatorial path model in representation theory. The aim is to merge various points of view on the geometric and topological construction of bases of representations of semisimple Lie algebras and their associated combinatorial models. One of these points of view is symplectic; it is based on the study of Mirković-Vilonen polytopes, which characterize one such basis and arise as the image under the momentum map of the relevant basis. Variational methods enter via Morse theory on loop groups.
Impressum Institution of DFG, MI University of Cologne, FM Ruhr-University Bochum and MI University of Heidelberg