Faces of weight polytopes and a generalization of a result of Vinberg

04/20/2010 - 12:15pm
04/20/2010 - 1:10pm
Tim Ridenour (UC Riverside)

This is a preliminary talk on results of joint work with V. Chari and A. Khare. We give an explicit description of the faces of the convex hull of the weights of Generalized Verma Modules for a semisimple Lie algebra g over C. Furthermore, we give a description of faces of certain polyhedra which is a generalization of Vinberg's description of faces of certain polytopes. We also use subsets of weights of finite dimensional irreducible highest weight modules that are contained in a proper face of the weight polytope to construct examples of Koszul algebras.

Millikan 208 (Pomona College)