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PBW filtration on highest weight representations

Algebra & Discrete Mathematics

Speaker: Teo Backhaus, University of Koeln (Cologne)
Location: 2112 MSB
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.