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Letters in Mathematical Physics

, Volume 78, Issue 1, pp 1–16 | Cite as

Verma Modules for Yangians

  • Y. Billig
  • V. Futorny
  • A. MolevEmail author
Article
  • 62 Downloads

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)).

Keywords

Yangian Verma module simple quotient 

Mathematics Subject Classification

81R10 

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Copyright information

© Springer 2006

Authors and Affiliations

  1. 1.School of Mathematics and StatisticsCarleton UniversityOttawaCanada
  2. 2.Instituto de Matematica e EstatisticaUniversidade de São PauloSao PauloBrazil
  3. 3.School of Mathematics and StatisticsUniversity of SydneySydneyAustralia

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