Automorphic Representations of \(\mathrm{GL}_{2}(\mathbb {A})\)

  • Anton Deitmar
Part of the Universitext book series (UTX)


In this chapter it is shown how the representation-theoretic interpretation of modular forms of Chap.  3 can be extended to the adelic setting. We thus interpret a modular form as a vector in a representation space of the adelic GL(2). We then need to show that any irreducible representation of the adelic GL(2) is a tensor product of local irreducible representations, which is known as the Tensor Product Theorem and generalizes the diagonalization of Hecke operators.


Irreducible Representation Modular Form Compact Group Haar Measure Cusp Form 
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Copyright information

© Springer-Verlag London 2013

Authors and Affiliations

  • Anton Deitmar
    • 1
  1. 1.Inst. MathematikUniversität TübingenTübingenGermany

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