Return to Colloquia & Seminar listing

### 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.