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PBW filtration and bases for irreducible modules in type A n

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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.

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Authors and Affiliations

  1. Department of Mathematics, University Higher School of Economics, 20 Myasnitskaya st., 101000, Moscow, Russia

    Evgeny Feigin

  2. Lebedev Physics Institute, Moscow, Russia

    Evgeny Feigin

  3. Mathematisches Institut, Universität zu Köln, Weyertal 86-90, D-50931, Köln, Germany

    Ghislain Fourier & Peter Littelmann

Authors
  1. Evgeny Feigin
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  2. Ghislain Fourier
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  3. Peter Littelmann
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Correspondence to Evgeny Feigin.

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Feigin, E., Fourier, G. & Littelmann, P. PBW filtration and bases for irreducible modules in type A n . Transformation Groups 16, 71–89 (2011). https://doi.org/10.1007/s00031-010-9115-4

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