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Verma Modules for Yangians

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Abstract

We study the Verma modules M((μu)) over the Yangian Y \((\mathfrak{a})\) associated with a simple Lie algebra \(\mathfrak{a}\). We give necessary and sufficient conditions for irreducibility of M(μ(u)). Moreover, regarding the simple quotient L((μu)) of M((μu)) as an \(\mathfrak{a}\)-module, we give necessary and sufficient conditions for finite-dimensionality of the weight subspaces of L((μu)).

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Authors and Affiliations

  1. School of Mathematics and Statistics, Carleton University, Ottawa, ON, K1S 5B6, Canada

    Y. Billig

  2. Instituto de Matematica e Estatistica, Universidade de São Paulo, CEP, 05315-970, Sao Paulo, Brazil

    V. Futorny

  3. School of Mathematics and Statistics, University of Sydney, Sydney, NSW, 2006, Australia

    A. Molev

Authors
  1. Y. Billig
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  2. V. Futorny
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  3. A. Molev
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Correspondence to A. Molev.

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Billig, Y., Futorny, V. & Molev, A. Verma Modules for Yangians. Lett Math Phys 78, 1–16 (2006). https://doi.org/10.1007/s11005-006-0107-1

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  • DOI: https://doi.org/10.1007/s11005-006-0107-1

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