PBW filtration and bases for irreducible modules in type $A_n$

Evgeny Feigin; Ghislain Fourier; Peter Littelmann

PBW filtration and bases for irreducible modules in type $A_n$

Representation Theory 2012-12-18 v3 Combinatorics

Authors: Evgeny Feigin , Ghislain Fourier , Peter Littelmann

Abstract

We study the PBW filtration on the highest weight representations $V(\la)$ of $\msl_{n+1}$ . 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 character formula for $V(\la)$ , and we obtain a new class of bases of the modules $V(\la)$ conjectured by Vinberg in 2005.

Keywords

PBW filtration highest weight representations Lie algebra sl_{n+1} associated graded module basis combinatorial character formula

Cite

@article{arxiv.1002.0674,
  title  = {PBW filtration and bases for irreducible modules in type $A_n$},
  author = {Evgeny Feigin and Ghislain Fourier and Peter Littelmann},
  journal= {arXiv preprint arXiv:1002.0674},
  year   = {2012}
}

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18 pages, references added

PBW filtration and bases for irreducible modules in type $A_n$

Abstract

Keywords

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