PBW filtration and bases for symplectic Lie algebras

Evgeny Feigin; Ghislain Fourier; Peter Littelmann

PBW filtration and bases for symplectic Lie algebras

Representation Theory 2012-12-18 v1 Combinatorics

Authors: Evgeny Feigin , Ghislain Fourier , Peter Littelmann

Abstract

We study the PBW filtration on the highest weight representations $V(\la)$ of $\msp_{2n}$ . This filtration is induced by the standard degree filtration on $U(\n^-)$ . We give a description of the associated graded $S(\n^-)$ -module $gr V(\la)$ in terms of generators and relations. We also construct a basis of $gr V(\la)$ . As an application we derive a graded combinatorial formula for the character of $V(\la)$ and obtain a new class of bases of the modules $V(\la)$ .

Keywords

PBW filtration symplectic Lie algebra highest weight representation associated graded module character formula basis construction

Cite

@article{arxiv.1010.2321,
  title  = {PBW filtration and bases for symplectic Lie algebras},
  author = {Evgeny Feigin and Ghislain Fourier and Peter Littelmann},
  journal= {arXiv preprint arXiv:1010.2321},
  year   = {2012}
}

Comments

21 pages

PBW filtration and bases for symplectic Lie algebras

Abstract

Keywords

Cite

Comments

Related papers