Symplectic Structures in Geometry, Algebra and Dynamics
Collaborative Research Centre TRR 191
 
A1, A2, A3, A5, A6, A7
B1, B2, B3, B4, B5, B6, B7
C1, C2, C3, C4, C5
Dynamics & Variational Methods
B4: Loop groups and the path model
Littelmann, Lytchak
Abstract:
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.
Group:
 
Prof. Peter Littelmann (PI)
mail: peter.littelmann at math.uni-koeln.de
phone: 0221 / 470 3715
room: 114
Mathematical Institute
University of Cologne
Prof. Alexander Lytchak (PI)
mail: alytchak at math.uni-koeln.de
phone: 0221 / 470 2888
room: 109
Mathematical Institute
University of Cologne
Valentin Rappel (ds)
mail: vrappel at math.uni-koeln.de
phone: 0221 / 470 4297
room: 212
Mathematical Institute
University of Cologne
Impressum Institution of DFG, MI University of Cologne and FM Ruhr-University Bochum