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Affine Lie algebras, theta functions and modular forms

  • Victor G. Kac
Part of the Progress in Mathematics book series (PM, volume 44)

Abstract

We begin this chapter with an exposition of a theory of theta functions. Using the classical transformation properties of theta functions and the theta function identity (12.7.13), we show that the string functions are modular forms and find a transformation law for these forms. Furthermore, using the theory of modular forms, we prove the “very strange” formula (12.3.7), which in turn, is used to show that the string functions, multiplied by a “standard” cusp-form, are cusp-forms. All this is applied to find explicit formulas for the weight multiplicities and characters of integrable highest weight modules.

Keywords

Holomorphic Function Modular Form Theta Function Finite Index Multiplier System 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Bibliographical notes and comments

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Copyright information

© Springer Science+Business Media New York 1983

Authors and Affiliations

  • Victor G. Kac
    • 1
  1. 1.Mathematics DepartmentMassachusetts Institute of TechnologyCambridgeUSA

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