Verma Modules II: Structure Theorem

  • Kenji Iohara
  • Yoshiyuki Koga
Part of the Springer Monographs in Mathematics book series (SMM)


The structure of Verma modules is analyzed in detail. Starting from the classification of the highest weights, the structure of the Jantzen filtration of Verma modules is completely determined from which the Bernstein−Gelfand−Gelfand type resolution follows. As a simple corollary, the characters of the all irreducible highest weight modules over Vir are given. In particular, the characters of minimal series representations, with fixed central charge, forms a vector-valued SL(2,ℤ)-modular form and its modular transformations are also calculated.


Modular Form Class Versus Singular Vector Normalise Character Structure Theorem 
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Copyright information

© Springer-Verlag London Limited 2011

Authors and Affiliations

  1. 1.Institut Camille JordanUniversité Claude Bernard Lyon 1Villeurbanne CedexFrance
  2. 2.Department of Applied Physics, Faculty of EngineeringUniversity of FukuiFukuiJapan

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