PBW filtration: Feigin-Fourier-Littelmann modules via Hasse diagrams

Abstract

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.

arXiv comment38 pages

References in corpus (5)

• Gelfand-Tsetlin polytopes and Feigin-Fourier-Littelmann polytopes as marked poset polytopes
• Extremal part of the PBW-filtration and E-polynomials
• Nonsymmetric Macdonald polynomials, Demazure modules and PBW filtration
• Realization of affine type A Kirillov-Reshetikhin crystals via polytopes
• Integrable systems, toric degenerations and Okounkov bodies

Cited by in corpus (6)

• Essential bases and toric degenerations arising from birational sequences
• Favourable modules: Filtrations, polytopes, Newton-Okounkov bodies and flat degenerations
• PBW-degenerated Demazure modules and Schubert varieties for triangular elements
• PBW-type filtration on quantum groups of type $A_n$
• The PBW filtration and convex polytopes in type $\mathtt{B}$
• A Continuous Family of Marked Poset Polytopes