Journal of Lie Theory

no. 3
PBW Filtration: Feigin-Fourier-Littelmann Modules Via Hasse Diagrams
Journal of Lie Theory, Volume 25 (2015) no. 3, pp. 815-856
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.
DOI: 10.5802/jolt.862
Classification: 06B15, 05E10, 17B10
Keywords: PBW filtration, FFL module, Hasse diagram, normal polytope 
@article{JOLT_2015_25_3_a9,
     author = {T. Backhaus and C. Desczyk},
     title = {PBW {Filtration:} {Feigin-Fourier-Littelmann} {Modules} {Via} {Hasse} {Diagrams}},
     journal = {Journal of Lie Theory},
     pages = {815--856},
     year = {2015},
     volume = {25},
     number = {3},
     doi = {10.5802/jolt.862},
     zbl = {1359.17018},
     url = {https://jolt.centre-mersenne.org/articles/10.5802/jolt.862/}
}
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T. Backhaus; C. Desczyk. PBW Filtration: Feigin-Fourier-Littelmann Modules Via Hasse Diagrams. Journal of Lie Theory, Volume 25 (2015) no. 3, pp. 815-856. doi: 10.5802/jolt.862

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