Classical automorphic forms and representations of SL ( 2 )
نویسنده
چکیده
This essay will explain the relationship between classical automorphic forms and representations of GL 2 (R). The classical theory of automorphic forms, in spite of initial appearances, is about the group GL 2 , not SL 2. The classical theory is concerned with functions on the upper half plane, which is acted on by fractional linear transformations in GL pos 2 (R), and it happens that the intersection of GL pos 2 (R) with GL 2 (Z) is SL 2 (Z). This accident is responsible for some mild confusion.
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