We will explain the notion of automorphic representation by considering the group GL(2) as an example. Without mentioning too many technical details, we will describe the adelization of this group, the basic principles of its local and global representation theory, and what makes a global representation "automorphic". Finally, we will show how one can "extract" an elliptic modular form from an automorphic representation, thus establishing a link between representation theory and classical modular forms.
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