Journal of Lie Theory 25 (2015), No. 3, 815--856
Copyright Heldermann Verlag 2015
PBW Filtration: Feigin-Fourier-Littelmann Modules Via Hasse Diagrams
Teodor Backhaus
Mathematisches Institut, Universität Köln, Weyertal 86-90, 50931 Köln, Germany
tbackha@math.uni-koeln.de
Chrisstian Desczyk
Mathematisches Institut, Universität Köln, Weyertal 86-90, 50931 Köln, Germany
cdesczyk@math.uni-koeln.de
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 parametrized 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. As an application we conclude that all representations considered in this paper are Feigin-Fourier-Littelmann modules.
Keywords: PBW filtration, FFL module, Hasse diagram, normal polytope.
MSC: 06B15, 05E10, 17B10
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