Geodesic
PBW Filtration: Feigin-Fourier-Littelmann Modules Via Hasse Diagrams
Teodor Backhaus1 ; Chrisstian Desczyk1
1Mathematisches Institut, Universität Köln, Weyertal 86-90, 50931 Köln, Germany
Journal of Lie Theory, Tome 25 (2015) no. 3, pp. 815-856

Voir la notice de l'article provenant de la source Heldermann Verlag

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.
Classification : 06B15, 05E10, 17B10
Mots-clés : PBW filtration, FFL module, Hasse diagram, normal polytope

Teodor Backhaus  1   ; Chrisstian Desczyk  1

1 Mathematisches Institut, Universität Köln, Weyertal 86-90, 50931 Köln, Germany 
Teodor Backhaus; Chrisstian Desczyk. PBW Filtration: Feigin-Fourier-Littelmann Modules Via Hasse Diagrams. Journal of Lie Theory, Tome 25 (2015) no. 3, pp. 815-856. http://geodesic.mathdoc.fr/item/JOLT_2015_25_3_a9/
@article{JOLT_2015_25_3_a9,
     author = {Teodor Backhaus and Chrisstian 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},
     url = {http://geodesic.mathdoc.fr/item/JOLT_2015_25_3_a9/}
}
TY  - JOUR
AU  - Teodor Backhaus
AU  - Chrisstian Desczyk
TI  - PBW Filtration: Feigin-Fourier-Littelmann Modules Via Hasse Diagrams
JO  - Journal of Lie Theory
PY  - 2015
SP  - 815
EP  - 856
VL  - 25
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/JOLT_2015_25_3_a9/
ID  - JOLT_2015_25_3_a9
ER  - 
%0 Journal Article
%A Teodor Backhaus
%A Chrisstian Desczyk
%T PBW Filtration: Feigin-Fourier-Littelmann Modules Via Hasse Diagrams
%J Journal of Lie Theory
%D 2015
%P 815-856
%V 25
%N 3
%U http://geodesic.mathdoc.fr/item/JOLT_2015_25_3_a9/
%F JOLT_2015_25_3_a9