Verma Modules I: Preliminaries
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.
KeywordsHigh Weight Integral Point Singular Vector Verma Module Conformal Weight
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