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Transformation Groups

, Volume 16, Issue 1, pp 71–89 | Cite as

PBW filtration and bases for irreducible modules in type A n

  • Evgeny FeiginEmail author
  • Ghislain Fourier
  • Peter Littelmann
Article

Abstract

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.

Keywords

Positive Root Simple Root Total Order Vertex Operator Algebra High Weight Vector 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  • Evgeny Feigin
    • 1
    • 2
    Email author
  • Ghislain Fourier
    • 3
  • Peter Littelmann
    • 3
  1. 1.Department of MathematicsUniversity Higher School of EconomicsMoscowRussia
  2. 2.Lebedev Physics InstituteMoscowRussia
  3. 3.Mathematisches InstitutUniversität zu KölnKölnGermany

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