AN ELEMENTARY INTRODUCTION TO THE LANGLANDS PROGRAM PDF

For example, in the work of Harish-Chandra one finds the principle that what can be done for one semisimple or reductive Lie group , should be done for all. The cusp form idea came out of the cusps on modular curves but also had a meaning visible in spectral theory as " discrete spectrum ", contrasted with the " continuous spectrum " from Eisenstein series. It becomes much more technical for bigger Lie groups, because the parabolic subgroups are more numerous. In all these approaches there was no shortage of technical methods, often inductive in nature and based on Levi decompositions amongst other matters, but the field was and is very demanding. There are many different groups over many different fields for which they can be stated, and for each field there are several different versions of the conjectures.

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