Polyhedral models of representation

• Applicant: Dr. Thomas Bliem
• Subject Area: Mathematics
• Term: from 2009 to 2011
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 127610340

The goal of the project is the development of combinatorial methods and their application in representation theory. The combinatorial side concerns the following problem: How many points with integral coordinates are contained in a given convex polytope? How does this number change if the sides of the polytope are displaced? Important figures in the representation theory of Lie algebras, the so-called weight multiplicities, can be encoded as families of polytopes obtained from one another by displacement of the sides. Thus, in the project, the existing methods for describing this combinatorial situation shall be further developed and exploited with respect to representation theory.

• DFG Programme: Priority Programmes
• Subproject of: SPP 1388: Representation Theory