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

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

2010-02-03

arxiv.org/abs/1002.0674v3

Mathematics

Representation Theory

18 pages, references added

Scientific paper

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.

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