PBW filtration on highest weight representationsAlgebra & Discrete Mathematics
|Speaker:||Teo Backhaus, University of Koeln (Cologne)|
|Start time:||Mon, Feb 9 2015, 5:10PM|
We study the PBW filtration on the irreducible highest weight representations of simple complex finite-dimensional Lie algebras. This filtration is induced by the standard degree filtration on the universal enveloping algebra. For certain rectangular weights we provide a new description of the associated graded module in terms of generators and relations. We also construct a basis parameterized by the integer points of a normal polytope. The main tool we use is the Hasse diagram defined via the standard partial order on the positive roots.