PBW filtration and bases for irreducible modules in type An

By Evgeny Feigin, Ghislain Fourier, P. Littelmann. 2010

139 citations recorded by the source corpus.

We study the PBW filtration on the highest weight representations V(λ) of $$ \mathfrak{s}{\mathfrak{l}_{n + 1}} $$. This filtration is induced by the standard degree filtration on $$ {\text{U}}\left( {{\mathfrak{n}^{-} }} \right) $$. We give a description of the associated graded $$ S\left( {{\mathfrak{n}^{-} }} \right) $$-module gr V(λ) in terms of generators and relations. We also construct a basis of gr V(λ). As an application we derive a graded combinatorial character formula for V(λ), and we obtain a new class of bases of the modules V(λ) conjectured by Vinberg in 2005.

Subfields: Discrete Mathematics and Combinatorics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/5ef83607921b9797ca5a7d3c7d0ef99ca5be05c2

Citations in the corpus

• Degenerate flag varieties of type A and C are Schubert varieties (2014, unknown): “For instance, they can be used to determine a q-character formula for characters of irreducible modules in type A [7, 8] and C [9, 10].”